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
Hauptverfasser: Liu, Huaifu, Mo, Xiaohuan, Zhu, Ling
Format: Artikel
Sprache:eng
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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.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-024-02252-x