The Morse Index for Manifolds with Constant Sectional Curvature
MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.21, no.4, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 21 Issue: 4
- Publication Date: 2024
- Doi Number: 10.1007/s00009-024-02682-5
- Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Middle East Technical University Affiliated: Yes
Abstract
We compute the Morse index of a critical submanifold of the energy functional on the loop space of a manifold with constant sectional curvature. The case of constant non-positive sectional curvature is a known result and the case of a sphere has been proved by Klingenberg. We adapt Klingenberg's proof of the case of a sphere to the case of constant sectional curvature, to obtain the possible Morse indices of critical submanifolds of the energy functional.