The Morse Index for Manifolds with Constant Sectional Curvature

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.

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

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Department of Economics, Article