Abstract
We observe that the maximal open set of constant curvature κ in a Riemannian manifold of curvature ≥ κ or 6 ≤ κ has a convexity-type property, which we call two-convexity. This statement is used to prove a number of rigidity statements in comparison geometry.
Original language | English (US) |
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Pages (from-to) | 617-631 |
Number of pages | 15 |
Journal | Geometry and Topology |
Volume | 18 |
Issue number | 2 |
DOIs | |
State | Published - Jan 30 2014 |
All Science Journal Classification (ASJC) codes
- Geometry and Topology