Universität zu Köln

Ivanov, Sergei and Lytchak, Alexander (2019). Rigidity of Busemann convex Finsler metrics. Comment. Math. Helv., 94 (4). S. 855 - 869. ZURICH: EUROPEAN MATHEMATICAL SOC. ISSN 1420-8946

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Ivanov, Sergei UNSPECIFIED UNSPECIFIED UNSPECIFIED Lytchak, Alexander UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-159703
DOI:	10.4171/CMH/476
Journal or Publication Title:	Comment. Math. Helv.
Volume:	94
Number:	4
Page Range:	S. 855 - 869
Date:	2019
Publisher:	EUROPEAN MATHEMATICAL SOC
Place of Publication:	ZURICH
ISSN:	1420-8946
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language BERWALD SPACES Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/15970