Invariant \((\alpha , \beta)\)-metrics on homogeneous manifolds
The \((\alpha, \beta)\)-metrics in Finsler geometry have been introduced by \textit{M. Matsumoto} [Rep. Math. Phys. 31, No.~1, 43--83 (1992; Zbl 0772.53009)]. The authors construct invariant \((\alpha, \beta)\)-metrics on a homogeneous manifold from an invariant Riemannian metric and a vector field. Then, they find necessary and sufficient conditions for an \((\alpha, \beta)\)-metric to be of Berwald type or of Douglas type on a particular homogeneous space. Finally, they state necessary and sufficient conditions for invariant Kropina metrics and invariant Matsumoto metrics to be Berwald metrics on a homogeneous manifold.
scientific article; zbMATH DE number 5553530