Isometric immersions in Minkowski spaces (Q2928502)

In Finsler geometry, the Minkowski space is a generalization of the Euclidean space. The paper is devoted to isometric immersions of Finsler manifolds in Minkowski spaces, in particular, minimal immersions. Section 2 (next to the introduction) is a brief motivation for Finsler geometry. In Section 3, a non-existence theorem on isometric immersions of Finsler manifolds into a Minkowski space is shown. Then the mean curvature of Finsler submanifolds is defined using the volume variation. Finsler submanifolds with vanishing mean curvature are called minimal submanifolds. In Section 4, it is shown that there is no compact minimal submanifold in the Minkowski space. A Bernstein theorem on Finsler minimal graphs in the Minkowski 3-space with respect to the Holmes-Thompson volume measure is given. Moreover, the second variation of the volume for minimal hypersurfaces in the Minkowski space is considered. In Section 5 minimal hypersurfaces in the (\(\alpha,\beta\))-Minkowski space are discussed. Some Bernstein-type theorems on complete minimal hypersurfaces in the (\(\alpha,\beta\))-Minkowski space are shown and some examples are given.NEWLINENEWLINEFor the entire collection see [Zbl 1291.00056].