On geodesics of Finsler metrics via navigation problem

DOI10.1090/S0002-9939-2011-10726-3zbMath1261.53037MaRDI QIDQ3020389

Libing Huang, Xiaohuan Mo

Publication date: 4 August 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Zermelo navigationFunk metricstrongly convex domain

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global submanifolds (53C40)

Related Items (19)

Generalized Zermelo navigation on Hermitian manifolds under mild wind ⋮ Isometries, submetries and distance coordinates on Finsler manifolds ⋮ On conformal vector fields on Randers manifolds ⋮ A Finsler geodesic spray paradigm for wildfire spread modelling ⋮ Isoparametric hypersurfaces induced by navigation in Lorentz Finsler geometry ⋮ The isoparametric functions on a class of Finsler spheres ⋮ Unnamed Item ⋮ Zermelo deformation of Hermitian metrics by holomorphic vector fields ⋮ Sharp uncertainty principles on general Finsler manifolds ⋮ On conformal fields of a Randers metric with isotropic \(S\)-curvature ⋮ On singular Finsler foliation ⋮ On some Finsler metrics of non-positive constant flag curvature ⋮ On some explicit constructions of dually flat Finsler metrics ⋮ Inner Radius Estimates and Rigidity for a Finsler Measure Space with Boundary ⋮ Geodesic orbit spheres and constant curvature in Finsler geometry ⋮ Finsler spaces whose geodesics are orbits ⋮ On the Landsberg curvature of a class of Finsler metrics generated from the navigation problem ⋮ On generalization of Zermelo navigation problem on Riemannian manifolds ⋮ ON SPHERICALLY SYMMETRIC FINSLER METRICS WITH ISOTROPIC BERWALD CURVATURE

Cites Work

• On Randers metrics with isotropic \(S\)-curvature
• On the Ricci curvature of a Randers metric of isotropic \(S\)-curvature
• A global classification result for Randers metrics of scalar curvature on closed manifolds
• Multiple closed geodesics on 3-spheres
• Zermelo navigation on Riemannian manifolds
• Two-dimensional Finsler metrics with constant flag curvature
• Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres
• The existence of two closed geodesics on every Finsler 2-sphere
• Geodesics in Randers spaces of constant curvature
• ON RANDERS METRICS OF QUADRATIC RIEMANN CURVATURE
• Finsler Metrics with K = 0 and S = 0
• The geometry of Hamilton and Lagrange spaces
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