From the Ricci flow evolution equation to vanishing theorems for Ricci solitons
Vladimir Rovenski, Sergey Stepanov, Irina Tsyganok
TL;DR
This paper investigates the evolution of scalar and Ricci curvatures under Ricci flow on various manifolds, identifying conditions for trivial flow and Ricci solitons to be Ricci flat or Einstein.
Contribution
It establishes new criteria linking Ricci flow evolution equations to vanishing theorems for Ricci solitons, extending understanding of their geometric properties.
Findings
Conditions for trivial Ricci flow on closed and noncompact manifolds.
Criteria for Ricci solitons to be Ricci flat or Einstein.
Insights into the evolution of curvature under Ricci flow.
Abstract
In the paper, we study evolution equations of the scalar and Ricci curvatures under the Hamilton's Ricci flow on a closed manifold and on a complete noncompact manifold. In particular, we study conditions when the Ricci flow is trivial and the Ricci soliton is Ricci flat or Einstein.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research