Counting closed geodesics on Riemannian manifolds

Eaman Eftekhary

Counting closed geodesics on Riemannian manifolds

Differential Geometry 2020-12-08 v2

Authors: Eaman Eftekhary

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 $g$ .

Keywords

closed geodesics riemannian manifolds geodesic count function locally constant function compact open subsets

Cite

@article{arxiv.1912.10740,
  title  = {Counting closed geodesics on Riemannian manifolds},
  author = {Eaman Eftekhary},
  journal= {arXiv preprint arXiv:1912.10740},
  year   = {2020}
}

Comments

The main result is slightly generalized, and some of the arguments are shortened in the revision. There are no major technical modifications

Counting closed geodesics on Riemannian manifolds

Abstract

Keywords

Cite

Comments

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