Sweeping out sectional curvature

Dmitri Panov, Anton Petrunin

Type: Article

Publication Date: 2014-01-30

Citations: 5

DOI: https://doi.org/10.2140/gt.2014.18.617

Abstract

We observe that the maximal open set of constant curvature Ä in a Riemannian manifold of curvature > Ä or 6 Ä has a convexity-type property, which we call two-convexity.This statement is used to prove a number of rigidity statements in comparison geometry.

Locations

arXiv (Cornell University) - View - PDF
Research Portal (King's College London) - View - PDF
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Geometry & Topology - View - PDF

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+	Rigidity of riemannian manifolds containing an equator	2020	Laurent Mazet
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Works Cited by This (13)

Action	Title	Year	Authors
+	Comparison Theorems in Riemannian Geometry	2008	Jeff Cheeger David G. Ebin
+	Examples of Riemannian Manifolds with non-negative sectional curvature	2007	Wolfgang Ziller
+	Diffeomorphism Finiteness, Positive Pinching, and Second Homotopy	1999	Anton Petrunin Wilderich Tuschmann
+ PDF Chat	Geometric curvature bounds in Riemannian manifolds with boundary	1993	Stephanie Alexander Ina Berg Richard L. Bishop
+ PDF Chat	Rigidity Theorems for Compact Manifolds with Boundary and Positive Ricci Curvature	2009	Fengbo Hang Xiaodong Wang
+	Scalar curvature rigidity of asymptotically hyperbolic spin manifolds	1989	Maung Min-Oo
+	Sign and geometric meaning of curvature	1991	M. Gromov
+ PDF Chat	On the long-time behavior of type-III Ricci flow solutions	2007	John Lott
+	Global and local curvatures	1996	Joachim Lohkamp
+ PDF Chat	Scalar curvature rigidity of certain symmetric spaces	1998	Maung Min-Oo