Morse estimates for translated points on unit tangent bundles

2022/05/27 by Simon Allais, Allais, Simon · 1 citation
Mathematics · #53C22 #53D25 #57R17 #58E10 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53C22 #msc:53D25 #msc:57R17 #msc:58E10

paper · pdf · doi:10.48550/arxiv.2205.13946

14 pages

arxiv created 2022/05/27 · arxiv updated 2022/05/30

Abstract

In this article, we study conjectures of Sandon on the minimal number of translated points in the special case of the unit tangent bundle of a Riemannian manifold. We restrict ourselves to contactomorphisms of SM that lift diffeomorphisms of M homotopic to identity. We prove that there exist sequences (p_n,t_n) where p_n is a translated point of time-shift t_n with t_n→+∞ for a large class of manifolds. We also prove Morse estimates on the number of translated points in the case of Zoll Riemannian manifolds.

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• On flat translated chains of contactomorphisms of ℝ²ⁿ⁺¹ and ℝ²ⁿ × S¹

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