On totally umbilical submanifolds of a locally Minkowski manifold (Q685929)

The complete totally umbilical (c.t.u.) submanifolds (whose induced and intrinsic connections coincide) of Finslerian manifolds are examined. Some results are the following: Any c.t.u. hypersurface \(M^ n\) of a locally Minkowski manifold has diameter \(\leq \pi/ \alpha_ 0\); for \(n=2\), \(M^ 2\) is totally geodesic or \(M^ 2\) is a Finsler space of negative scalar curvature \(\alpha^ 2_ 0\). Some results for umbilical CR submanifolds are obtained.