Geodesic
Finsler Metrics with K = 0 and S = 0
Canadian journal of mathematics, Tome 55 (2003) no. 1, pp. 112-132

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2003-005-6
Mots-clés : 53C60, 53B40 
Shen, Zhongmin. Finsler Metrics with K = 0 and S = 0. Canadian journal of mathematics, Tome 55 (2003) no. 1, pp. 112-132. doi: 10.4153/CJM-2003-005-6
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