Characterizing round spheres using half-geodesics-Reference-Cited by-同舟云学术

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Characterizing round spheres using half-geodesics

Published:2019-07-01 Issue:29 Volume:116 Page:14501-14504
ISSN:0027-8424
Container-title:Proceedings of the National Academy of Sciences
language:en
Short-container-title:Proc Natl Acad Sci USA

Author:

Adelstein Ian M.,Schmidt Benjamin

Abstract

A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this paper establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round.

Publisher

Proceedings of the National Academy of Sciences

Subject

Multidisciplinary

Reference13 articles.

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2. Variational problems on closed manifolds;Lyusternik;Doklady Akad. Nauk SSSR (N.S.),1951

3. A. L. Besse , Manifolds all of Whose Geodesics are Closed (Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics, Springer-Verlag, Berlin, 1978), Vol. 93.

4. On metrics on S 2 all of whose geodesics are closed;Gromoll;Invent. Math.,1981/82

5. On the Berger conjecture for manifolds all of whose geodesics are closed;Radeschi;Invent. Math.,2017

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1. Besse Projective Spaces with Many Diameters;The Journal of Geometric Analysis;2023-06-17

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