Finsler Metrics with <b>K</b> = 0 and <b>S</b> = 0

2003/02/01 by Zhongmin Shen · 9 citations
Physics and Astronomy · #Advanced Differential Geometry Research

paper · pdf · doi:10.4153/cjm-2003-005-6

Abstract

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.

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• Wind Finslerian Structures: From Zermelo’s Navigation to the Causality of Spacetimes
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• Failure of famous functional inequalities on Finsler manifolds: the influence of S-curvature
• Sharp uncertainty principles on general Finsler manifolds
• Characteristic tensors for almost Finsler manifolds
• On the flag curvature of Finsler metrics of scalar curvature
• Time-dependent Zermelo navigation with tacking
• Analogue Gravity and Trans-Atlantic Air Travel
• Geodesics in Randers spaces of constant curvature
• Two-dimensional Finsler metrics with constant flag curvature

Related

• Finsler metrics of weakly isotropic flag curvature
• The Randers metrics of weakly isotropic scalar curvature
• Finsler Metrics with K=0 and S=0
• A class of Randers metrics of scalar flag curvature
• On the flag curvature of Finsler metrics of scalar curvature