The second closed geodesic, the fundamental group, and generic Finsler metrics

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The second closed geodesic, the fundamental group, and generic Finsler metrics. / Rademacher, Hans Bert; Taimanov, Iskander A.

In: Mathematische Zeitschrift, Vol. 302, No. 1, 09.2022, p. 629-640.

Research output: Contribution to journal › Article › peer-review

Harvard

Rademacher, HB & Taimanov, IA 2022, 'The second closed geodesic, the fundamental group, and generic Finsler metrics', Mathematische Zeitschrift, vol. 302, no. 1, pp. 629-640. https://doi.org/10.1007/s00209-022-03062-z

APA

Rademacher, H. B., & Taimanov, I. A. (2022). The second closed geodesic, the fundamental group, and generic Finsler metrics. Mathematische Zeitschrift, 302(1), 629-640. https://doi.org/10.1007/s00209-022-03062-z

Vancouver

Rademacher HB, Taimanov IA. The second closed geodesic, the fundamental group, and generic Finsler metrics. Mathematische Zeitschrift. 2022 Sept;302(1):629-640. doi: 10.1007/s00209-022-03062-z

Author

Rademacher, Hans Bert ; Taimanov, Iskander A. / The second closed geodesic, the fundamental group, and generic Finsler metrics. In: Mathematische Zeitschrift. 2022 ; Vol. 302, No. 1. pp. 629-640.

BibTeX

@article{30bbc7f1cd034091a0d15cfaabd18108,

title = "The second closed geodesic, the fundamental group, and generic Finsler metrics",

abstract = "For compact manifolds with infinite fundamental group we present sufficient topological or metric conditions ensuring the existence of two geometrically distinct closed geodesics. We also extend results about generic Riemannian metrics to Finsler metrics. We show a bumpy metrics theorem for Finsler metrics and prove that a C4-generic Finsler metric on a compact and simply-connected manifold carries infinitely many closed geodesics.",

keywords = "Closed geodesic, Finsler metric, Fundamental group, Generic metric",

author = "Rademacher, {Hans Bert} and Taimanov, {Iskander A.}",

note = "Funding Information: I. A. Taimanov was supported by Russian Science Foundation (Grant 19-11-00044) Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2022",

month = sep,

doi = "10.1007/s00209-022-03062-z",

language = "English",

volume = "302",

pages = "629--640",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - The second closed geodesic, the fundamental group, and generic Finsler metrics

AU - Rademacher, Hans Bert

AU - Taimanov, Iskander A.

PY - 2022/9

Y1 - 2022/9

N2 - For compact manifolds with infinite fundamental group we present sufficient topological or metric conditions ensuring the existence of two geometrically distinct closed geodesics. We also extend results about generic Riemannian metrics to Finsler metrics. We show a bumpy metrics theorem for Finsler metrics and prove that a C4-generic Finsler metric on a compact and simply-connected manifold carries infinitely many closed geodesics.

AB - For compact manifolds with infinite fundamental group we present sufficient topological or metric conditions ensuring the existence of two geometrically distinct closed geodesics. We also extend results about generic Riemannian metrics to Finsler metrics. We show a bumpy metrics theorem for Finsler metrics and prove that a C4-generic Finsler metric on a compact and simply-connected manifold carries infinitely many closed geodesics.

KW - Closed geodesic

KW - Finsler metric

KW - Fundamental group

KW - Generic metric

UR - http://www.scopus.com/inward/record.url?scp=85133620681&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=49158362

U2 - 10.1007/s00209-022-03062-z

DO - 10.1007/s00209-022-03062-z

M3 - Article

AN - SCOPUS:85133620681

VL - 302

SP - 629

EP - 640

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 1

ER -

ID: 36771813