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 journal › Article › peer-review
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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