Generalized Berwald metrics

In this paper, we consider a class of Finsler metrics called generalized Berwald metrics which contains the class of Berwald metrics as a special case. We prove that every generalized Berwald metrics with non-zero scalar flag curvature or isotropic Berwald curvature is a Randers metric. Then we prove that on generalized Berwald metrics, the notions of generalized Landsberg and Landsberg curvatures are equivalent.

Anahtar Kelimeler:

Berwald metric, landsberg metric, randers metric

Generalized Berwald metrics

Keywords:

Berwald metric, landsberg metric, randers metric,

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Department of Mathematics, Faculty of Science Arak University, Arak, 38156-8-8349, IRAN e-mail: epeyghan@gmail.com Akbar TAYEBI
Department of Mathematics, Faculty of Science Qom University, Qom-IRAN e-mail: akbar.tayebi@gmail.com