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Projectively flat Finsler metrics of constant flag curvature

Author(s): Zhongmin Shen
Journal: Trans. Amer. Math. Soc. 355 (2003), 1713-1728.
MSC (2000): Primary 53C60, 53A20
Posted: December 2, 2002
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Abstract: Finsler metrics on an open subset in ${R}^n$ 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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Additional Information:

Zhongmin Shen
Affiliation: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216
Email: zshen@math.iupui.edu

DOI: 10.1090/S0002-9947-02-03216-6
PII: S 0002-9947(02)03216-6
Received by editor(s): July 1, 2002
Posted: December 2, 2002
Copyright of article: Copyright 2002, American Mathematical Society

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