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On a Class of Projectively Flat Metrics with Constant Flag Curvature |
Canad. J. Math. 60(2008), 443-456
Published:2008-04-01
Printed: Apr 2008
Printed: Apr 2008
- Z. Shen
- G. Civi Yildirim
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) |