On a Class of Projectively Flat Metrics with Constant Flag Curvature

Shen, Z. ; Yildirim, G. Civi

Canadian journal of mathematics, Tome 60 (2008) no. 2, pp. 443-456

Résumé

In this paper, we find equations that characterize locally projectively flat Finsler metrics in the form $F\,=\,{{(\alpha \,+\,\beta )}^{2}}/\alpha $ where $\alpha \,=\,\sqrt{{{a}_{ij}}{{y}^{i}}{{y}^{j}}}$ is a Riemannian metric and $\beta \,=\,{{b}_{i}}{{y}^{i}}$ is a 1-form. Then we completely determine the local structure of those with constant flag curvature.

Détail

DOI : 10.4153/CJM-2008-021-1

Mots-clés : 53B40

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