Projectively flat Finsler metrics of constant flag curvature

Shen, Zhongmin

doi:10.1090/S0002-9947-02-03216-6

Projectively flat Finsler metrics of constant flag curvature
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by Zhongmin Shen

Trans. Amer. Math. Soc. 355 (2003), 1713-1728

DOI: https://doi.org/10.1090/S0002-9947-02-03216-6

Published electronically: December 2, 2002

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Abstract:

Finsler metrics on an open subset in $\mathrm {R}^n$ with straight geodesics are said to be projective. It is known that the flag curvature of any projective Finsler metric is a scalar function of tangent vectors (the flag curvature must be a constant if it is Riemannian). In this paper, we discuss the classification problem on projective Finsler metrics of constant flag curvature. We express them by a Taylor expansion or an algebraic formula. Many examples constructed in this paper can be used as models in Finsler geometry.

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