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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, 53B40 show english descriptions Finsler spaces and generalizations (areal metrics) [See also 58B20]
Finsler spaces and generalizations (areal metrics)
53C60 - Finsler spaces and generalizations (areal metrics) [See also 58B20]
53B40 - Finsler spaces and generalizations (areal metrics)
 

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