ZERMELO DEFORMATION OF FINSLER METRICS BY KILLING VECTOR FIELDS

Patrick Foulon (1) , Vladimir Matveev (2)

1 CIRM - Centre International de Rencontres Mathématiques
2 Friedrich-Schiller-Universität = Friedrich Schiller University Jena [Jena, Germany]

We show how geodesics, Jacobi vector fields, and flag curvature of a Finsler metric behave under Zermelo deformation with respect to a Killing vector field. We also show that Zermelo deformation with respect to a Killing vector field of a locally symmetric Finsler metric is also locally symmetric.

Domaines: Mathématiques [math]; Géométrie différentielle [math.DG]; Systèmes dynamiques [math.DS]

Patrick Foulon, Vladimir Matveev. ZERMELO DEFORMATION OF FINSLER METRICS BY KILLING VECTOR FIELDS. Communications in Mathematical Sciences, 2018, 25, pp.1935 - 9179. ⟨10.3934/era.2018.25.001⟩. ⟨hal-02361840⟩