Projectively flat Finsler spaces with \((\alpha{},\beta{})\)-metric
The \((\alpha,\beta)\)-metric is a Finsler metric which is constructed from a Riemannian metric \(\alpha\) and a differential 1-form \(\beta\). A Finsler space is called projectively flat, or with rectilinear geodesic, if the space is covered by coordinate neighbourhoods in which the geodesics can be represented by \(n-1\) linear equations of the coordinates. Such a coordinate system is called rectilinear. In the present paper the author considers the projective flatness of Finsler spaces with \((\alpha,\beta)\)-metric. Projective flatness of the Kropina space and a special generalized Kropina space are also studied.
scientific article; zbMATH DE number 89979
scientific article