Ricci flow on modified Riemann extensions
H. G. Nagaraja, Harish D
TL;DR
This paper investigates how modified Riemann extensions evolve under Ricci flow, providing conditions for their preservation and analyzing curvature tensor behavior during the flow.
Contribution
It establishes necessary and sufficient conditions for modified Riemann extensions to remain as such under Ricci flow and explores curvature tensor properties during the evolution.
Findings
Derived conditions for preservation of modified Riemann extensions under Ricci flow
Analyzed the behavior of curvature tensors during Ricci flow
Provided insights into the geometric evolution of these extensions
Abstract
We study the properties of Modified Riemann extensions evolving under Ricci flow. We obtain the necessary and sufficient condition for modified Riemann extension under Ricci flow to stay as modified Riemann extension. We also discuss the properties of the curvature tensors under Ricci flow.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds