Date

2024-06-01

Author

Şirikçi, Nil İpek

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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.

Subject Keywords

Morse index, constant sectional curvature, Riemannian geometry

URI

https://hdl.handle.net/11511/109935

Collections

Department of Economics, Article