On the geometry of Einstein-type manifolds with some structural conditions
Gabjin Yun, Seungsu Hwang
TL;DR
This paper explores the geometric properties of Einstein-type manifolds, unifying various structures and establishing rigidity results under specific curvature conditions.
Contribution
It introduces a unified framework for Einstein-type equations and proves new rigidity theorems based on curvature assumptions.
Findings
Rigidity results for Einstein-type manifolds under curvature conditions
Unification of critical point and vacuum static equations
New geometric insights into Einstein-type structures
Abstract
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation. We show various rigidity results of Einstein-type manifolds under assumptions of several curvature conditions.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Fixed Point Theorems Analysis