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.
PEYGHAN, ESMAEIL and TAYEBI, AKBAR
"Generalized Berwald metrics,"
Turkish Journal of Mathematics: Vol. 36:
3, Article 13.
Available at: https://journals.tubitak.gov.tr/math/vol36/iss3/13