## As their applications, we obtain Liouville type theorems for positive or bounded solutions to the above equation when either F = cu(1 − u) (the Fisher-KKP equation) or; F = −u3 + u (the Allen–Cahn equation); or $F=au\log u$ (the equation involving gradient Ricci solitons). 作为它们的应用，当 F = cu(1 − u) （Fisher-KKP 方程）或F = -u3 + u（艾伦-卡恩方程）；或 $F=au\log u$ （涉及梯度 Ricci 孤子的方程）。

Gradient Estimates for a Class of Semilinear Parabolic Equations and Their Applications

## In the present paper, first, we characterize the standard static spacetimes satisfying certain Ricci-Hessian class type equations, such as generalized quasi Einstein manifolds, m-quasi Einstein manifolds, ( m , ρ ) -quasi Einstein manifolds, and gradient Ricci solitons. 在本文中，首先，我们描述了满足某些 Ricci-Hessian 类类型方程的标准静态时空，例如广义拟爱因斯坦流形、m-拟爱因斯坦流形、( m , ρ ) -拟爱因斯坦流形和梯度 Ricci 孤子。

On generalized quasi Einstein standard static spacetimes

## For self-similar configurations, such equations describe generalized Ricci solitons defining modified Einstein equations. 对于自相似配置，此类方程描述了广义 Ricci 孤子，定义了改进的爱因斯坦方程。

Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

## In this vein, we characterize trivial generalized Ricci solitons. 在这方面，我们描述了平凡的广义 Ricci 孤子。

A Note on Solitons with Generalized Geodesic Vector Field

## In this paper we give new Gaussian type upper bounds for the Schrodinger heat kernel on complete gradient shrinking Ricci solitons with the scalar curvature bounded above. 在本文中，我们给出了完全梯度收缩 Ricci 孤子上薛定谔热核的新高斯型上界，标量曲率在上界。

Schrödinger heat kernel upper bounds on gradient shrinking Ricci solitons

## In this paper, we prove an n-dimensional radially flat gradient shrinking Ricci solitons with $$div^2W(\nabla f,\nabla f)=0$$ is rigid. 在本文中，我们证明了一个 n 维径向平面梯度收缩 Ricci 孤子，$$div^2W(\nabla f,\nabla f)=0$$ 是刚性的。

On Gradient Shrinking Ricci Solitons with Radial Conditions

## The purpose of this paper is to investigate some equations of structure for h -almost Ricci soliton which are a natural generalization for almost Ricci solitons.

Some results on h-almost Ricci solitons

## Almost Ricci-harmonic solitons are generalization of Ricci-harmonic solitons, almost Ricci solitons and harmonic-Einstein metrics.

Gap theorems for compact almost Ricci-harmonic solitons

## In this paper we study Ricci solitons in generalized D-conformally deformed Kenmotsu manifold and we analyzed the nature of Ricci solitons when associated vector field is orthagonal to Reeb vector field.

Ricci Solitons in Kenmotsu Manifold under Generalized D-Conformal Deformation

## The object of this paper is to study Ricci solitons under some curvature conditions in nearly cosymplectic manifolds.

Some Results on Nearly Cosymplectic Manifolds

## We complete the classification of Ricci solitons within all classes of homogeneous Siklos metrics. 我们完成了所有类同质 Siklos 度量中的 Ricci 孤子分类。

The Ricci soliton equation for homogeneous Siklos spacetimes

## We determine and describe all the Ricci solitons within a very large class of Siklos metrics. 我们确定并描述了一个非常大的 Siklos 度量标准中的所有 Ricci 孤子。

Solutions of the Ricci soliton equation for a large class of Siklos spacetimes

## We complete the classification of Ricci solitons within all classes of homogeneous Siklos metrics. 我们完成了所有类同质 Siklos 度量中的 Ricci 孤子分类。

The Ricci soliton equation for homogeneous Siklos spacetimes

## Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. 许多作者在（几乎）接触几何的框架内研究了里奇孤子及其类似物。

On non-gradient $$(m,\rho )$$ ( m , ρ ) -quasi-Einstein contact metric m

## The objective of present research article is to investigate the geometric properties of $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds. 本研究文章的目的是研究洛伦兹 para-Kenmotsu 流形上 $\eta$-Ricci 孤子的几何性质。

ETA-RICCI SOLITONS ON LORENTZIAN PARA-KENMOTSU MANIFOLDS

## Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly  symmetric trans-Sasakian manifolds. 此外，他们还证明了 Ricci 孤子、η-Ricci 孤子和三维弱  对称 trans-Sasakian 流形的一些结果。

Three-dimensional trans-Sasakian manifolds and solitons

## We develop a variational method to find pseudo-algebraic Ricci solitons on connected Lie groups. 我们开发了一种变分方法来找到连通李群上的伪代数 Ricci 孤子。

Pseudo-algebraic Ricci solitons on Einstein nilradicals

## This paper is concerned with the study of [Formula: see text]-manifolds and Ricci solitons. 本文关注[公式：见正文]-流形和里奇孤子的研究。

LCS-manifolds and Ricci solitons

10.1140/epjc/s10052-020-08798-8

## For self-similar configurations, such equations describe generalized Ricci solitons defining modified Einstein equations. 对于自相似配置，此类方程描述了广义 Ricci 孤子，定义了改进的爱因斯坦方程。

Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows

## In this paper we give new Gaussian type upper bounds for the Schrodinger heat kernel on complete gradient shrinking Ricci solitons with the scalar curvature bounded above. 在本文中，我们给出了完全梯度收缩 Ricci 孤子上薛定谔热核的新高斯型上界，标量曲率在上界。

Schrödinger heat kernel upper bounds on gradient shrinking Ricci solitons

## We verify the extension to the zero section of momentum construction of Kaehler-Einstein metrics and Kaehler-Ricci solitons on the total space Y of positive rational powers of the canonical line bundle of toric Fano manifolds with possibly irregular Sasaki-Einstein metrics. 我们验证了 Kaehler-Einstein 度量和 Kaehler-Ricci 孤子在正有理次方正有理次幂的总空间 Y 上的扩展，该空间 Y 具有可能不规则的 Sasaki-Einstein 度量的复曲面 Fano 流形的规范线束。

Irregular Eguchi–Hanson type metrics and their soliton analogues

## Then we investigate Ricci solitons on recurrent curvature Lie groups. 然后我们研究了循环曲率李群上的 Ricci 孤子。

On Lie Groups with Recurrent Curvature in Dimension Four

10.31926/but.mif.2020.13.62.2.16

## We prove that the scalar curvature of an N(k)-paracontact metric manifold admitting η-Ricci solitons is constant and the manifold is of constant curvature k. 我们证明了一个允许 η-Ricci 孤子的 N(k)-paracontact 度量流形的标量曲率是恒定的，并且流形具有恒定的曲率 k。

N(k)-paracontact three metric as a Eta-Ricci soliton

## As their applications, we obtain Liouville type theorems for positive or bounded solutions to the above equation when either F = cu(1 − u) (the Fisher-KKP equation) or; F = −u3 + u (the Allen–Cahn equation); or $F=au\log u$ (the equation involving gradient Ricci solitons). 作为它们的应用，当 F = cu(1 − u) （Fisher-KKP 方程）或F = -u3 + u（艾伦-卡恩方程）；或 $F=au\log u$ （涉及梯度 Ricci 孤子的方程）。

Gradient Estimates for a Class of Semilinear Parabolic Equations and Their Applications

10.20944/PREPRINTS202102.0053.V1

## 3D Ricci solitons projection via a semi-conformal mapping to a surface is also studied. 还研究了通过半保形映射到表面的 3D Ricci 孤子投影。

Sliding Mode Control and Geometrization Conjecture in Seismology

## Motivated by this result, we classify codimension one subgroups of the solvable Iwasawa groups of irreducible symmetric spaces of non-compact type whose induced metrics are Ricci solitons. 受此结果的启发，我们对非紧致型不可约对称空间的可解 Iwasawa 群的余维一子群进行分类，其诱导度量为 Ricci 孤子。

Codimension one Ricci soliton subgroups of solvable Iwasawa groups

## In the present paper, first, we characterize the standard static spacetimes satisfying certain Ricci-Hessian class type equations, such as generalized quasi Einstein manifolds, m-quasi Einstein manifolds, ( m , ρ ) -quasi Einstein manifolds, and gradient Ricci solitons. 在本文中，首先，我们描述了满足某些 Ricci-Hessian 类类型方程的标准静态时空，例如广义拟爱因斯坦流形、m-拟爱因斯坦流形、( m , ρ ) -拟爱因斯坦流形和梯度 Ricci 孤子。

On generalized quasi Einstein standard static spacetimes

## ‎,‎ ‎homogeneous‎ ‎Ricci solitons and harmonicity properties of invariant vector fields‎. ‎,‎ ‎homogeneous‎ ‎Ricci 孤子和不变向量场的谐波特性‎。

Some geometrical properties of Berger Spheres

## We use a semiclassical version of the Nexus paradigm of quantum gravity in which the quantum vacuum at large scales is dominated by the second quantized electromagnetic field to demonstrate that a virtual photon field can affect the geometric evolution of Einstein manifolds or Ricci solitons. 我们使用量子引力的 Nexus 范式的半经典版本，其中大尺度的量子真空由第二量子化电磁场支配，以证明虚拟光子场可以影响爱因斯坦流形或 Ricci 孤子的几何演化。

On the Electromagnetic Vacuum Origins of Dark Energy, Dark Matter, and Astrophysical Jets

## In this vein, we characterize trivial generalized Ricci solitons. 在这方面，我们描述了平凡的广义 Ricci 孤子。

A Note on Solitons with Generalized Geodesic Vector Field

## Spaces of this type include diverse interesting classes: gradient Ricci solitons, $m$-quasi Einstein metrics, (vacuum) static spaces, $V$-static spaces, and critical point metrics. 这种类型的空间包括各种有趣的类：梯度 Ricci 孤子、$m$-拟爱因斯坦度量、（真空）静态空间、$V$-静态空间和临界点度量。

Three-dimensional Ricci-degenerate Riemannian manifolds satisfying geometric equations

## The setting generalizes various previously studied situations; for instance, Ricci solitons, Ricci harmonic solitons, generalized quasi-Einstein manifolds and so on. 该设置概括了以前研究过的各种情况；例如，里奇孤子、里奇谐波孤子、广义准爱因斯坦流形等。

On the geometry of Einstein-type structures

## The proofs stem from the construction of gradient Ricci solitons that are realized as warped products, from which we know that the base spaces of these products are Ricci-Hessian type manifolds. 证明源于梯度 Ricci 孤子的构造，这些孤子被实现为翘曲产品，从中我们知道这些产品的基空间是 Ricci-Hessian 型流形。

A note on gradient Ricci soliton warped metrics

## Moreover, Ricci solitons on Ricci flat, concircularly flat, M -projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. 此外，还研究了承认上述联系的跨Sasakian流形的Ricci平面、同圆平面、M-射影平面和伪射影平面反不变子流形上的Ricci孤子。

Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold

## (4), ‎space is expanding Ricci solitons‎. (4)、“空间正在扩大里奇孤子”。

Exact solutions of Diffusion Equation on sphere

## In this paper, we investigate invariant Ricci solitons, an important subclass in the class of homogeneous Ricci solitons. 在本文中，我们研究了不变量 Ricci 孤子，它是同质 Ricci 孤子类中的一个重要子类。

Invariant Ricci Solitons on Three-Dimensional Metric Lie Groups with Semi-Symmetric Connection

## We establish the geometrical bearing on Legendrian submanifolds of Sasakian space forms in terms of r-almost Newton–Ricci solitons (r-anrs) with the potential function $$\psi : M^{n} \rightarrow \mathcal {R}$$. 我们用势函数 $$\psi : M^{n} \rightarrow \mathcal {R}$$ 的 r-几乎牛顿-里奇孤子 (r-anrs) 来建立 Sasakian 空间形式的 Legendrian 子流形的几何方位.

r-Almost Newton–Ricci solitons on Legendrian submanifolds of Sasakian space forms

## Applications of such submanifolds to Ricci solitons and Yamabe solitons has also been showed. 这种子流形在 Ricci 孤子和 Yamabe 孤子中的应用也得到了展示。

Submanifolds of Sasakian Manifolds with Concurrent Vector Field

## We determine and describe all the Ricci solitons within a very large class of Siklos metrics. 我们确定并描述了一个非常大的 Siklos 度量标准中的所有 Ricci 孤子。

Solutions of the Ricci soliton equation for a large class of Siklos spacetimes

## Next, we characterize Ricci solitons on 3-dimensional Riemannian manifolds and gradient Ricci almost solitons on a Riemannian manifold (of dimension n) admitting a concurrent-recurrent vector field. 接下来，我们描述了 3 维黎曼流形上的 Ricci 孤子和允许并发循环向量场的黎曼流形（维数 n）上的梯度 Ricci 几乎孤子。

Ricci solitons on Riemannian manifolds admitting certain vector field

## Biconformal deformations in the presence of a conformal foliation by curves are exploited to study equivalence between 3-dimensional Ricci solitons. 利用曲线存在共形叶理的双共形变形来研究 3 维 Ricci 孤子之间的等价性。

Biconformal equivalence between 3-dimensional Ricci solitons

## Ricci solitons, which R. Ricci 孤子，其中 R.

Conformally Killing Fields on 2-Symmetric Five-Dimensional Lorentzian Manifolds

## In this paper, we prove an n-dimensional radially flat gradient shrinking Ricci solitons with $$div^2W(\nabla f,\nabla f)=0$$ is rigid. 在本文中，我们证明了一个 n 维径向平面梯度收缩 Ricci 孤子，$$div^2W(\nabla f,\nabla f)=0$$ 是刚性的。

On Gradient Shrinking Ricci Solitons with Radial Conditions

## In this paper, we study an almost coKahler manifold admitting certain metrics such as $$*$$ -Ricci solitons, satisfying the critical point equation (CPE) or Bach flat. 在本文中，我们研究了一个近似 coKahler 流形，它承认某些指标，例如 $$*$$ -Ricci 孤子，满足临界点方程 (CPE) 或 Bach flat。

Certain types of metrics on almost coKähler manifolds

## The aim of the present research article is to study the f-kenmotsu manifolds admitting the η-Ricci Solitons and gradient Ricci solitons with respect to the semi-symmetric non metric connection. 本研究文章的目的是研究关于半对称非度量连接的 f-kenmotsu 流形，该流形承认 η-Ricci 孤子和梯度 Ricci 孤子。

η-Ricci Solitons and Gradient Ricci Solitons on f-Kenmotsu Manifolds

## In this paper, we classify affine Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections and perturbed canonical connections and perturbed Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure. 在本文中，我们对具有某些乘积结构的三维洛伦兹李群上的正则连接和小林-野水连接以及扰动正则连接和扰动小林-野水连接相关的仿射里奇孤子进行分类。

Affine Ricci Solitons of Three-Dimensional Lorentzian Lie Groups

## In the present paper, we study curvature properties of η-Ricci solitons on para-Kenmotsu manifolds.

Curvature Properties of 𝜂-Ricci Solitons on Para-Kenmotsu Manifolds

## In this paper, we first completely determine all left-invariant generalized Ricci solitons on the Heisenberg group $$H_{2n+1}$$H2n+1 equipped with any left-invariant Riemannian and Lorentzian metric that this Lie group admits.

On the Geometry of Higher Dimensional Heisenberg Groups

## In this paper, we prove that any complete shrinking gradient Kähler–Ricci solitons with positive orthogonal bisectional curvature must be compact.

Gradient Kähler–Ricci Solitons with Nonnegative Orthogonal Bisectional Curvature

## In this paper we study Ricci solitons in generalized D-conformally deformed Kenmotsu manifold and we analyzed the nature of Ricci solitons when associated vector field is orthagonal to Reeb vector field.

Ricci Solitons in Kenmotsu Manifold under Generalized D-Conformal Deformation

## We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds with Codazzi type of the Ricci tensor.

Eta-Ricci solitons on LP-Sasakian manifolds

## The object of the present research is to study the (ϵ,δ)-Trans Sasakian manifolds addmitting the η-Ricci Solitons.

η-RICCI SOLITONS IN (ϵ,δ)-TRANS SASAKIAN MANIFOLDS

## In this paper, we study the geometry and topology of η-Ricci solitons satisfying Ricci-semisymmetry condition, S ⋅ R = 0 condition and finally Einstein-semisymmetry condition on nearly Kenmotsu man.

η-Ricci solitons on nearly Kenmotsu manifolds

## The purpose of the paper is to study *-Ricci solitons and *-gradient Ricci solitons on three-dimensional normal almost contact metric manifolds.

*-Ricci Solitons on Three-dimensional Normal Almost Contact Metric Manifolds

## In this short note, we prove a non-existence result for $$*$$∗-Ricci solitons on non-cosymplectic $$(\kappa ,\mu )$$(κ,μ)-almost cosymplectic manifolds.

Non-existence of $$*$$∗-Ricci solitons on $$(\kappa ,\mu )$$(κ,μ)-almost cosymplectic manifolds

## The object of the present paper is to investigate the nature of Ricci solitons on D-homothetically deformed Kenmotsu manifold with generalized weakly symmetric and generalized weakly Ricci symmetric curvature restrictions.

Ricci solitons in a generalized weakly (Ricci) symmetric D-homothetically deformed Kenmotsu manifold

## Several geometric properties such as being conformally flat, existing Ricci solitons and Walker structures are exhibited.

Ricci solitons and geometry of four dimensional Einstein-like neutral Lie groups

## Among others, Ricci solitons of such notions have been investigated.

Warped product CR-submanifolds of Sasakian manifolds with respect to certain connections

## In this paper, inspired by Fernandez-Lopez and Garcia-Rio [11] , we shall give a new lower diameter bound for compact non-trivial shrinking Ricci solitons depending on the range of the potential function, as well as on the range of the scalar curvature.

Remark on a lower diameter bound for compact shrinking Ricci solitons

## In this paper we study the nature of Ricci solitons in D-homo-thetically deformed Kenmotsu manifolds.

D-Homothetically Deformed Kenmotsu Metric as a Ricci Soliton

## The purpose of this paper is to investigate some equations of structure for h -almost Ricci soliton which are a natural generalization for almost Ricci solitons.

Some results on h-almost Ricci solitons

## Section V treats curvature functionals and Ricci solitons.

A Survey of Riemannian Contact Geometry

## We prove rigidity theorems for shrinking gradient Ricci solitons supporting the Heisenberg-Pauli-Weyl uncertainty principle with the sharp constant in $\mathbb{R}^n$.

Uncertainty Principle and its rigidity on complete gradient shrinking Ricci solitons

## Almost Ricci-harmonic solitons are generalization of Ricci-harmonic solitons, almost Ricci solitons and harmonic-Einstein metrics.

Gap theorems for compact almost Ricci-harmonic solitons

## We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein.

On Shrinking Gradient Ricci Solitons with Positive Ricci Curvature and Small Weyl Tensor

## The object of the present paper is to characterize $$\epsilon$$ϵ-Kenmotsu manifolds admitting $$\eta$$η-Ricci solitons.

$$\eta$$η-Ricci solitons in $$\epsilon$$ϵ-Kenmotsu manifolds

## Also we study (Error rendering LaTeX formula) -Ricci solitons on three-dimensional (Error rendering LaTeX formula) -paracontact metric manifolds.

Certain results on (Error rendering LaTeX formula) -paracontact metric manifolds

10.4067/s0719-06462019000300063

## In this paper we characterize the Sasakian 3-manifolds admitting β-almost Ricci solitons whose potential vector field is a contact vector field.

Beta-almost Ricci solitons on Sasakian 3-manifolds

## In this work, we give some basic informations about Ricci solitons on a nearly Kenmotsu manifold and some structures on this manifolds satisfying semi-symmetric metric connection.

Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection

## We consider almost η-Ricci solitons in (e)-para Sasakian manifolds satisfying certain curvature conditions.

Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds

## The object of this paper is to study Ricci solitons under some curvature conditions in nearly cosymplectic manifolds.

Some Results on Nearly Cosymplectic Manifolds

## Ricci Solitons 里奇孤子

Ricci Solitons 里奇孤子
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