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Finsler Metrics with K = 0 and S = 0

Published online by Cambridge University Press:  20 November 2018

Zhongmin Shen*
Affiliation:
Math. Dept., IUPUI, 402 N. Blackford Street, Indianapolis, IN 46202-3216, USA, email: [email protected]
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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

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2003

References

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