A Class of Projectively Flat Finsler Metrics
Projectively flat Finlser metrics on a convex domain U in R n are regular solutions to Hilbert’s Fourth Problem. In this paper, we study projectively flat Finlser metrics on U . We find equations that characterize these metrics with weakly orthogonal invariance, refining a theorem due to Sol o ´ rza...
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Veröffentlicht in: | Resultate der Mathematik 2024-09, Vol.79 (6), Article 226 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | Projectively flat Finlser metrics on a convex domain
U
in
R
n
are regular solutions to Hilbert’s Fourth Problem. In this paper, we study projectively flat Finlser metrics on
U
. We find equations that characterize these metrics with weakly orthogonal invariance, refining a theorem due to Sol
o
´
rzano-Le
o
´
n. As its application, we obtain infinitely many
new
projectively flat Finlser metrics on
S
n
+
1
and determine their scalar flag curvature. These metrics contain Bryant’s projective spherically symmetric Finsler metric of constant flag curvature 1. |
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ISSN: | 1422-6383 1420-9012 |
DOI: | 10.1007/s00025-024-02252-x |