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Finsler Metrics with ${\bf K}=0$ and ${\bf S}=0$

Published:2003-02-01
Printed: Feb 2003
• Zhongmin Shen
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Abstract

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.
 MSC Classifications: 53C60 - Finsler spaces and generalizations (areal metrics) [See also 58B20] 53B40 - Finsler spaces and generalizations (areal metrics)