Morse Index bound of simple closed geodesics on 2-spheres and strong Morse Inequalities

Dongyeong Ko

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arXiv · 2303.00644

Morse Index bound of simple closed geodesics on 2-spheres and strong Morse Inequalities

Dongyeong Ko

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Abstract

We give a Morse-theoretic characterization of simple closed geodesics on Riemannian $2$-spheres. On any Riemannian $2$-sphere endowed with a generic metric, we show there exists a simple closed geodesic with Morse index $1$, $2$ and $3$. In particular, for an orientable Riemannian surface we prove strong Morse inequalities for the length functional applied to the space of simple closed curves.

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Dongyeong Ko. 2023-03-01. Morse Index bound of simple closed geodesics on 2-spheres and strong Morse Inequalities. https://arxiv.org/abs/2303.00644

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