
TL;DR
This paper extends Myers' theorem to certain Riemannian manifolds with conditions involving the Bismut-Witten Laplacian and a curvature function, providing new criteria for finiteness of the fundamental group.
Contribution
It introduces new curvature conditions involving the Bismut-Witten Laplacian that extend classical Myers' theorem to broader classes of manifolds.
Findings
Manifolds with $ ho^h$ satisfying $ riangle^h - ho^h < 0$ have finite fundamental group.
Provides a quick proof of recent Myers' theorem extensions.
Includes results applicable to noncompact manifolds.
Abstract
Let be a compact Riemannian manifold and a smooth function on . Let . Here denotes the Ricci curvature at and is the Hessian of . Then has finite fundamental group if . Here is the Bismut-Witten Laplacian. This leads to a quick proof of recent results on extension of Myers' theorem to manifolds with mostly positive curvature. There is also a similar result for noncompact manifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds
