Geometry & Topology
- Geom. Topol.
- Volume 18, Number 2 (2014), 617-631.
Sweeping out sectional curvature
We observe that the maximal open set of constant curvature in a Riemannian manifold of curvature or has a convexity-type property, which we call two-convexity. This statement is used to prove a number of rigidity statements in comparison geometry.
Geom. Topol., Volume 18, Number 2 (2014), 617-631.
Received: 29 March 2013
Revised: 7 September 2013
Accepted: 28 September 2013
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C24: Rigidity results
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Panov, Dmitri; Petrunin, Anton. Sweeping out sectional curvature. Geom. Topol. 18 (2014), no. 2, 617--631. doi:10.2140/gt.2014.18.617. https://projecteuclid.org/euclid.gt/1513732754