Local Rigidity of Convex Hypersurfaces in Spaces of Constant Curvature
Abstract
In this paper, we prove a local rigidity of convex hypersurfaces in the spaces of constant curvature of dimension n ≥ 4. Namely, we show that two isometric convex hypersurfaces are congruent locally around their corresponding under the isometry points of strict convexity.This result extends the result of E.P. Senkin, who showed such rigidity under the additional assumption of C 1 -smoothness of the hypersurfaces.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Geometric and Algebraic Topology
Publication details
- Journal / source
- Zurnal matematiceskoj fiziki analiza geometrii
- Volume
- 22
- Issue
- 1
- Pages
- 22–33
- Publication date
- 25 January 2026
- Language
- EN