Counting closed geodesics on Riemannian manifolds

2019/12/23 by Eftekhary, Eaman
#37C10 #53C22 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.10740

Abstract

Fix a smooth closed manifold M. Let R_M denote the space of all pairs (g,L) such that g is a C³ Riemannian metric on M and the real number L is not the length of any closed g-geodesics. A locally constant geodesic count function π_M:R_M→ 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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