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Finsler Metrics with K = 0 and S = 0

Published online by Cambridge University Press:  20 November 2018

Zhongmin Shen
Zhongmin Shen*
Affiliation:
Math. Dept., IUPUI, 402 N. Blackford Street, Indianapolis, IN 46202-3216, USA, email: zshen@math.iupui.edu
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Abstract

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In the paper, we study the shortest time problem on a Riemannian space with an external force. We show that such problem can be converted to a shortest path problem on a Randers space. By choosing an appropriate external force on the Euclidean space, we obtain a non-trivial Randers metric of zero flag curvature. We also show that any positively complete Randers metric with zero flag curvature must be locally Minkowskian.

Keywords

53C6053B40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 1 , 01 February 2003 , pp. 112 - 132
Copyright
Copyright © Canadian Mathematical Society 2003

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