Finsler Metrics with K = 0 and S = 0

2003/02/01 by Zhongmin Shen · 136 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebra over a field #Computer science #Curvature #Euclidean distance #Flag (linear algebra) #Geometry #Mathematical analysis #Mathematics #Metric (unit) #Path (computing) #Pure mathematics #Space (punctuation) #Zero (linguistics)

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

published in Canadian Journal of Mathematics 55(1), 112-132 (Cambridge University Press)

openalex publication_date 2003/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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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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