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arXiv · 1912.10740

Counting closed geodesics on Riemannian manifolds

Eaman Eftekhary
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Abstract

Fix a smooth closed manifold $M$. Let $R_M$ denote the space of all pairs $(g,L)$ such that $g$ is a $C^3$ Riemannian metric on $M$ and the real number $L$ is not the length of any closed $g$-geodesics. A locally constant geodesic count function $\pi_M:R_M\rightarrow Z$ is constructed. For this purpose, the weight of compact open subsets of the space of closed $g$-geodesics is defined and investigated for an arbitrary Riemannian metric $g$.

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Eaman Eftekhary. 2019-12-23. Counting closed geodesics on Riemannian manifolds. https://arxiv.org/abs/1912.10740

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