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The Cotton Tensor and the Ricci Flow [PDF]
Geometric Flows, 2017 AbstractWe compute the evolution equation of the Cotton and the Bach tensor under the Ricci flow of a Riemannian manifold, with particular attention to the three dimensional case, and we discuss some applications.
Carlo Mantegazza +2 more
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Producing 3D Ricci flows with nonnegative Ricci curvature via singular Ricci flows [PDF]
Geometry & Topology, 2021 We extend the concept of singular Ricci flow by Kleiner and Lott from 3d compact manifolds to 3d complete manifolds with possibly unbounded curvature. As an application of the generalized singular Ricci flow, we show that for any 3d complete Riemannian manifold with non-negative Ricci curvature, there exists a smooth Ricci flow starting from it.
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The Soliton-Ricci Flow with variable volume forms
Complex Manifolds, 2016 We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the ...
Pali Nefton
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Metric Perspectives of the Ricci Flow Appliedto Disjoint Unions
Analysis and Geometry in Metric Spaces, 2014 In this paper we consider compact, Riemannian manifolds M1, M2 each equipped with a oneparameterfamily of metrics g1(t), g2(t) satisfying the Ricci flow equation.
Lakzian Sajjad, Munn Michael
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Ancient solutions to the Ricci flow in dimension $3$ [PDF]
Acta Mathematica, 2018 It is known from work of Perelman that any finite-time singularity of the Ricci flow on a compact three-manifold is modeled on an ancient $\kappa$-solution.
S. Brendle
semanticscholar +1 more source
On the stability of harmonic maps under the homogeneous Ricci flow
Complex Manifolds, 2018 In this work we study properties of stability and non-stability of harmonic maps under the homogeneous Ricci flow.We provide examples where the stability (non-stability) is preserved under the Ricci flow and an example where the Ricci flow does not ...
Prado Rafaela F. do, Grama Lino
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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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Local mollification of Riemannian metrics using Ricci flow, and Ricci limit spaces [PDF]
Geometry and Topology, 2017 We use Ricci flow to obtain a local bi-Holder correspondence between Ricci limit spaces in three dimensions and smooth manifolds. This is more than a complete resolution of the three-dimensional case of the conjecture of Anderson-Cheeger-Colding-Tian ...
Miles Simon, P. Topping
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