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Characterizations of Trivial Ricci Solitons
Advances in Mathematical Physics, 2020 Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton.
Sharief Deshmukh +2 more
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A MECHANICS FOR THE RICCI FLOW
International Journal of Geometric Methods in Modern Physics, 2009 We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time-dependent Hamilton–Jacobi equation of the mechanics so defined.
Abraham, S. +3 more
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Ricci Soliton and Certain Related Metrics on a Three-Dimensional Trans-Sasakian Manifold
Universe, 2022 In this article, a Ricci soliton and *-conformal Ricci soliton are examined in the framework of trans-Sasakian three-manifold. In the beginning of the paper, it is shown that a three-dimensional trans-Sasakian manifold of type (α,β) admits a Ricci ...
Zhizhi Chen +4 more
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Communications on Pure and Applied Mathematics, 2012 AbstractIn this paper, we study the moduli spaces of m‐dimensional, κ‐noncollapsed Ricci flow solutions with bounded $\int |Rm|^{{m}/{2}}$ and bounded scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study the estimates of isoperimetric constants, the Kähler‐Ricci flows, and the moduli spaces of gradient ...
Chen, Xiuxiong, Wang, Bing
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The spinorial energy for asymptotically Euclidean Ricci flow
Advanced Nonlinear Studies, 2023 This article introduces a functional generalizing Perelman’s weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well defined on a wide class of noncompact manifolds; on asymptotically Euclidean manifolds, the functional is shown
Baldauf Julius, Ozuch Tristan
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A modified Kähler–Ricci flow [PDF]
Mathematische Annalen, 2009 In this note, a modified Kähler-Ricci flow is introduced and studied. The main point is to show the flexibility of Kähler-Ricci flow and summarize some useful techniques.
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Heat Kernel Estimate Along Ricci-Harmonic Flow
MathematicsIn this paper, we study the Ricci-harmonic flow under the assumption that the scalar curvature is bounded. First, we establish a time-derivative bound for solutions to the heat equation along the flow.
Chen Wang, Guoqiang Wu
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Ricci-Bourgoignon Flow on Contact Manifolds
پژوهشهای ریاضی, 2020 Introduction After pioneering work of Hamilton in 1982, Ricci flow and other geometric flows became as one of the most interesting topics in both mathematics and physics.
Ghodratallah Fasihi-Ramandi +1 more
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Stability of Kähler-Ricci Flow [PDF]
Journal of Geometric Analysis, 2009 We prove the convergence of Kähler-Ricci flow with some small initial curvature conditions. As applications, we discuss the convergence of Kähler-Ricci flow when the complex structure varies on a Kähler-Einstein manifold.
Chen, Xiuxiong, Li, Haozhao
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Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures
, 2022 In this paper, we study the monotonicity of parabolic frequency motivated by \cite{frequency on RF} under the Ricci flow and the Ricci-harmonic flow on manifolds. Here we consider two cases: one is the monotonicity of parabolic frequency for the solution
Xu, Kairui, Li, Chuanhuan, Li, Yi
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