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On a Class of Projectively Flat Metrics with Constant Flag Curvature

  • Z. Shen (a1) and G. Civi Yildirim (a2)

Abstract

In this paper, we find equations that characterize locally projectively flat Finsler metrics in the form $F\,=\,{{(\alpha \,+\,\beta )}^{2}}/\alpha $ where $\alpha \,=\,\sqrt{{{a}_{ij}}{{y}^{i}}{{y}^{j}}}$ 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.

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References

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On a Class of Projectively Flat Metrics with Constant Flag Curvature

  • Z. Shen (a1) and G. Civi Yildirim (a2)

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