Submanifolds in Finsler spaces of scalar-curvature
The author proves the following four theorems: a. If \(M^ n\) is a totally geodesic submanifold of a Finsler space of scalar curvature, then \(M^ n\) is a Finsler space of scalar curvature, too. b. If \(M^ n\) is a totally umbilical submanifold of a Finsler space, then the mean curvature is v-parallel, where v denotes the intrinsic Finsler vector field. The induced and intrinsic connections of \(M_ n\) coincide. c. If \(M^ n\) is a totally-geodesic submanifold of a locally Minkowski space, then \(M_ n\) is a locally Minkowski space, too. d. Let \(M^ 2\) be a closed umbilical Landsberg surface in the Finsler space \(M^ 3(c)\) of positive scalar curvature. If the induced and intrinsic connection of \(M^ 2\) coincide then \(\chi (M^ 2)\neq 0\), where \(\chi (M^ 2)\) is the Euler- Poincaré characteristic of \(M^ 2\).
scientific article; zbMATH DE number 4151271