The weighted connection and sectional curvature for manifolds with density
| Autor: | Lee Kennard, William Wylie, Dmytro Yeroshkin |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics 010102 general mathematics Rauch comparison theorem 01 natural sciences Convexity Connection (mathematics) Perspective (geometry) 53C20 53C25 Differential geometry Differential Geometry (math.DG) 0103 physical sciences FOS: Mathematics Sphere theorem 010307 mathematical physics Geometry and Topology Sectional curvature Mathematics::Differential Geometry 0101 mathematics Symmetry (geometry) Mathematics |
| DOI: | 10.48550/arxiv.1707.05376 |
| Popis: | In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion-free connection introduced recently by the last two authors. We develop two new tools for studying weighted sectional curvature bounds: a new weighted Rauch comparison theorem and a modified notion of convexity for distance functions. As applications we prove generalizations of theorems of Preissman and Byers for negative curvature, the (homeomorphic) quarter-pinched sphere theorem, and Cheeger’s finiteness theorem. We also improve results of the first two authors for spaces of positive weighted sectional curvature and symmetry. |
| Databáze: | OpenAIRE |
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