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Rigidity of Busemann convex Finsler metrics. / Ivanov, Sergei ; Lytchak, Alexander.

In: Commentarii Mathematici Helvetici, Vol. 94, No. 4, 18.12.2019, p. 855-868.

Research output: Contribution to journalArticlepeer-review

Harvard

Ivanov, S & Lytchak, A 2019, 'Rigidity of Busemann convex Finsler metrics', Commentarii Mathematici Helvetici, vol. 94, no. 4, pp. 855-868. https://doi.org/10.4171/CMH/476

APA

Ivanov, S., & Lytchak, A. (2019). Rigidity of Busemann convex Finsler metrics. Commentarii Mathematici Helvetici, 94(4), 855-868. https://doi.org/10.4171/CMH/476

Vancouver

Ivanov S, Lytchak A. Rigidity of Busemann convex Finsler metrics. Commentarii Mathematici Helvetici. 2019 Dec 18;94(4):855-868. https://doi.org/10.4171/CMH/476

Author

Ivanov, Sergei ; Lytchak, Alexander. / Rigidity of Busemann convex Finsler metrics. In: Commentarii Mathematici Helvetici. 2019 ; Vol. 94, No. 4. pp. 855-868.

BibTeX

@article{1a1d35c0a8244f27a46486e87fda8506,
title = "Rigidity of Busemann convex Finsler metrics",
abstract = "We prove that a Finsler metric is nonpositively curved in the sense of Busemann if and only if it is affinely equivalent to a Riemannian metric of nonpositive sectional curvature. In other terms, such Finsler metrics are precisely Berwald metrics of nonpositive flag curvature. In particular in dimension 2 every such metric is Riemannian or locally isometric to that of a normed plane. In the course of the proof we obtain new characterizations of Berwald metrics in terms of the so-called linear parallel transport.",
keywords = "Non-positive curvature, Busemann convex space, Berwald metric",
author = "Sergei Ivanov and Alexander Lytchak",
note = "Ivanov Sergei, Lytchak Alexander: Rigidity of Busemann convex Finsler metrics. Comment. Math. Helv. 94 (2019), 855-868. doi: 10.4171/CMH/476",
year = "2019",
month = dec,
day = "18",
doi = "10.4171/CMH/476",
language = "English",
volume = "94",
pages = "855--868",
journal = "Commentarii Mathematici Helvetici",
issn = "0010-2571",
publisher = "European Mathematical Society Publishing House",
number = "4",

}

RIS

TY - JOUR

T1 - Rigidity of Busemann convex Finsler metrics

AU - Ivanov, Sergei

AU - Lytchak, Alexander

N1 - Ivanov Sergei, Lytchak Alexander: Rigidity of Busemann convex Finsler metrics. Comment. Math. Helv. 94 (2019), 855-868. doi: 10.4171/CMH/476

PY - 2019/12/18

Y1 - 2019/12/18

N2 - We prove that a Finsler metric is nonpositively curved in the sense of Busemann if and only if it is affinely equivalent to a Riemannian metric of nonpositive sectional curvature. In other terms, such Finsler metrics are precisely Berwald metrics of nonpositive flag curvature. In particular in dimension 2 every such metric is Riemannian or locally isometric to that of a normed plane. In the course of the proof we obtain new characterizations of Berwald metrics in terms of the so-called linear parallel transport.

AB - We prove that a Finsler metric is nonpositively curved in the sense of Busemann if and only if it is affinely equivalent to a Riemannian metric of nonpositive sectional curvature. In other terms, such Finsler metrics are precisely Berwald metrics of nonpositive flag curvature. In particular in dimension 2 every such metric is Riemannian or locally isometric to that of a normed plane. In the course of the proof we obtain new characterizations of Berwald metrics in terms of the so-called linear parallel transport.

KW - Non-positive curvature

KW - Busemann convex space

KW - Berwald metric

U2 - 10.4171/CMH/476

DO - 10.4171/CMH/476

M3 - Article

VL - 94

SP - 855

EP - 868

JO - Commentarii Mathematici Helvetici

JF - Commentarii Mathematici Helvetici

SN - 0010-2571

IS - 4

ER -

ID: 49986724