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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Projectively flat Finsler metrics of constant flag curvature
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by Zhongmin Shen PDF
Trans. Amer. Math. Soc. 355 (2003), 1713-1728 Request permission


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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Additional Information
  • Zhongmin Shen
  • Affiliation: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216
  • Email:
  • Received by editor(s): July 1, 2002
  • Published electronically: December 2, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 1713-1728
  • MSC (2000): Primary 53C60, 53A20
  • DOI:
  • MathSciNet review: 1946412