A Riemannian Plane With Only Two Injective Geodesics-Reference-Cited by-同舟云学术

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A Riemannian Plane With Only Two Injective Geodesics

Published:2023-08-10 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bangert Victor¹,Suhr Stefan²

Affiliation:

1. Mathematisches Institut, Abteilung für Reine Mathematik, Albert-Ludwigs-Universität Freiburg , Ernst-Zermelo-Straße 1, 79104 Freiburg, Germany

2. Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstraße 150 , 44780 Bochum, Germany

Abstract

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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnad180/51079476/rnad180.pdf

Reference14 articles.

1. Geodesics and totally convex sets on surfaces;Bangert;Invent. Math.,1981

2. On the existence of escaping geodesics;Bangert;Comment. Math. Helv.,1981

3. Geodätische Linien auf Riemannschen Mannigfaltigkeiten;Bangert;Jahresber. Dtsch. Math.-Ver.,1985

4. Min-max embedded geodesic lines in asymptotically conical surfaces;Carlotto;J. Differential Geom.,2019

5. Kürzeste Wege und Totalkrümmung auf Flächen;Cohn-Vossen;Compositio Math.,1935

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