Rigidity of compact rank one symmetric spaces
Abstract
Abstract We consider rigidity properties of compact symmetric spaces X with metric $$g_0$$ g 0 of rank one. Suppose g is another Riemannian metric on X with sectional curvature $$\kappa $$ κ bounded by $$0 \le \kappa \le 1.$$ 0 ≤ κ ≤ 1 . If g equals $$g_0$$ g 0 outside a convex proper subset of X , then g is isometric with $$g_0.$$ g 0 . We also exhibit examples of surfaces showing that the nonnegativity of the curvature is needed. Our main result complements earlier results on other symmetric spaces by Gromov and Schroeder–Ziller.
Fields of Study & Subjects
Advanced Algebra and Geometry
Advanced Topics in Algebra
Finite Group Theory Research
Publication details
- Journal / source
- Mathematische Annalen
- Volume
- 395
- Issue
- 3
- Publication date
- 28 May 2026
- Language
- EN