Ricci Solitons(里奇孤子)研究综述
Ricci Solitons 里奇孤子 - We complete the classification of Ricci solitons within all classes of homogeneous Siklos metrics. [1] Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. [2] The objective of present research article is to investigate the geometric properties of $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds. [3] Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly symmetric trans-Sasakian manifolds. [4] We develop a variational method to find pseudo-algebraic Ricci solitons on connected Lie groups. [5] This paper is concerned with the study of [Formula: see text]-manifolds and Ricci solitons. [6] For self-similar configurations, such equations describe generalized Ricci solitons defining modified Einstein equations. [7] 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. [8] 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. [9] Then we investigate Ricci solitons on recurrent curvature Lie groups. [10] 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. [11] 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). [12] 3D Ricci solitons projection via a semi-conformal mapping to a surface is also studied. [13] 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. [14] 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. [15] , homogeneous Ricci solitons and harmonicity properties of invariant vector fields. [16] 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. [17] In this vein, we characterize trivial generalized Ricci solitons. [18] 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. [19] The setting generalizes various previously studied situations; for instance, Ricci solitons, Ricci harmonic solitons, generalized quasi-Einstein manifolds and so on. [20] 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. [21] 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. [22] (4), space is expanding Ricci solitons. [23] In this paper, we investigate invariant Ricci solitons, an important subclass in the class of homogeneous Ricci solitons. [24] 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 $$\psi : M^{n} \rightarrow \mathcal {R}$$. [25] Applications of such submanifolds to Ricci solitons and Yamabe solitons has also been showed. [26] We determine and describe all the Ricci solitons within a very large class of Siklos metrics. [27] 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. [28] Biconformal deformations in the presence of a conformal foliation by curves are exploited to study equivalence between 3-dimensional Ricci solitons. [29] Ricci solitons, which R. [30] In this paper, we prove an n-dimensional radially flat gradient shrinking Ricci solitons with $$div^2W(\nabla f,\nabla f)=0$$ is rigid. [31] 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. [32] 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. [33] 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. [34] In the present paper, we study curvature properties of η-Ricci solitons on para-Kenmotsu manifolds. [35] 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. [36] In this paper, we prove that any complete shrinking gradient Kähler–Ricci solitons with positive orthogonal bisectional curvature must be compact. [37] 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. [38] We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds with Codazzi type of the Ricci tensor. [39] The object of the present research is to study the (ϵ,δ)-Trans Sasakian manifolds addmitting the η-Ricci Solitons. [40] 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. [41] The purpose of the paper is to study *-Ricci solitons and *-gradient Ricci solitons on three-dimensional normal almost contact metric manifolds. [42] In this short note, we prove a non-existence result for $$*$$∗-Ricci solitons on non-cosymplectic $$(\kappa ,\mu )$$(κ,μ)-almost cosymplectic manifolds. [43] 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. [44] Several geometric properties such as being conformally flat, existing Ricci solitons and Walker structures are exhibited. [45] Among others, Ricci solitons of such notions have been investigated. [46] 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. [47] In this paper we study the nature of Ricci solitons in D-homo-thetically deformed Kenmotsu manifolds. [48] 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. [49] Section V treats curvature functionals and Ricci solitons. [50]我们完成了所有类同质 Siklos 度量中的 Ricci 孤子分类。 [1] 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。 [2] 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。 [3] 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。 [4] 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。 [5] 本文关注[公式：见正文]-流形和里奇孤子的研究。 [6] 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。 [7] 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。 [8] 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。 [9] 然后我们研究了循环曲率李群上的 Ricci 孤子。 [10] 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。 [11] 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）。 [12] 还研究了通过半保形映射到表面的 3D Ricci 孤子投影。 [13] 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。 [14] 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。 [15] , homogeneous Ricci 孤子和不变向量场的谐波特性。 [16] 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。 [17] 在这方面，我们描述了平凡的广义 Ricci 孤子。 [18] 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。 [19] 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。 [20] 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。 [21] 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。 [22] (4)、“空间正在扩大里奇孤子”。 [23] 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。 [24] 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. [25] 这种子流形在 Ricci 孤子和 Yamabe 孤子中的应用也得到了展示。 [26] 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。 [27] 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。 [28] 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。 [29] Ricci 孤子，其中 R. [30] 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。 [31] 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。 [32] 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。 [33] 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。 [34] nan [35] nan [36] nan [37] nan [38] nan [39] nan [40] nan [41] nan [42] nan [43] nan [44] nan [45] nan [46] nan [47] nan [48] nan [49] nan [50]
Gradient Ricci Solitons
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). [1] 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. [2] 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. [3] 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. [4] 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. [5] The purpose of the paper is to study *-Ricci solitons and *-gradient Ricci solitons on three-dimensional normal almost contact metric manifolds. [6] We prove rigidity theorems for shrinking gradient Ricci solitons supporting the Heisenberg-Pauli-Weyl uncertainty principle with the sharp constant in $\mathbb{R}^n$. [7] We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. [8]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）。 [1] 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。 [2] 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。 [3] 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。 [4] 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。 [5] nan [6] nan [7] nan [8]
Generalized Ricci Solitons
For self-similar configurations, such equations describe generalized Ricci solitons defining modified Einstein equations. [1] In this vein, we characterize trivial generalized Ricci solitons. [2] 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. [3]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。 [1] 在这方面，我们描述了平凡的广义 Ricci 孤子。 [2] nan [3]
Shrinking Ricci Solitons
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. [1] In this paper, we prove an n-dimensional radially flat gradient shrinking Ricci solitons with $$div^2W(\nabla f,\nabla f)=0$$ is rigid. [2] 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. [3]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。 [1] 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。 [2] nan [3]
Almost Ricci Solitons
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. [1] Almost Ricci-harmonic solitons are generalization of Ricci-harmonic solitons, almost Ricci solitons and harmonic-Einstein metrics. [2] In this paper we characterize the Sasakian 3-manifolds admitting β-almost Ricci solitons whose potential vector field is a contact vector field. [3]Study Ricci 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. [1] The object of this paper is to study Ricci solitons under some curvature conditions in nearly cosymplectic manifolds. [2]ricci solitons within
We complete the classification of Ricci solitons within all classes of homogeneous Siklos metrics. [1] We determine and describe all the Ricci solitons within a very large class of Siklos metrics. [2]我们完成了所有类同质 Siklos 度量中的 Ricci 孤子分类。 [1] 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。 [2]