A Riemannian plane with only two injective Geodesics

2022/08/17 by Bangert, Victor, Suhr, Stefan
#53C22 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.08475

Abstract

We present an example of a complete Riemannian plane with precisely two injective geodesics - up to reparameterization. The example arises as a perturbation of a surface of revolution with contracting end. The last section is devoted to open problems.

Related

• Angle contraction between geodesics
• The geometry of a Randers rotational surface
• Closed geodesics on incomplete surfaces
• The second closed geodesic on Finsler spheres of dimension n>2
• Simple geodesics on a punctured surface