On Closed Geodesics in Non-negatively Curved Finsler Structures with Large Volume Growth

Sajjad Lakzian

On Closed Geodesics in Non-negatively Curved Finsler Structures with Large Volume Growth

Differential Geometry 2019-01-24 v3

Authors: Sajjad Lakzian

Abstract

We prove that a reversible Berwaldian Finsler structure $\left(M,F\right)$ with base-independent non-negative radial flag curvature and large volume growth does not have any closed geodesics.

Keywords

closed geodesics Finsler structure Berwald space flag curvature volume growth non-negative curvature

Cite

@article{arxiv.1408.0214,
  title  = {On Closed Geodesics in Non-negatively Curved Finsler Structures with Large Volume Growth},
  author = {Sajjad Lakzian},
  journal= {arXiv preprint arXiv:1408.0214},
  year   = {2019}
}

Comments

This paper is being withdrawn since our use of the comparison theorem for Finsler spaces was incorrect. However, we note that our conjecture was later proven by Martin Kell

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