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On a Class of Projectively Flat Metrics with Constant Flag Curvature

Published:2008-04-01
Printed: Apr 2008
• Z. Shen
• G. Civi Yildirim
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Abstract

In this paper, we find equations that characterize locally projectively flat Finsler metrics in the form $F = (\alpha + \beta)^2/\alpha$, where $\alpha=\sqrt{a_{ij}y^iy^j}$ 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.
 MSC Classifications: 53B40 - Finsler spaces and generalizations (areal metrics)