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Minimal submanifolds in general (α,β)-spaces

Songting Yin;  Qun He;  Dinghe Xie — 2013

Annales Polonici Mathematici

The volume forms of general (α,β)-metrics are studied. Some equations for minimal submanifolds in general (α,β)-spaces are established by using the normal frame field, and some minimal surfaces in general (α,β)-spaces with special curvature properties are constructed.

On totally umbilical submanifolds of Finsler spaces

Qun He;  Wei Yang;  Wei Zhao — 2011

Annales Polonici Mathematici

The notion of a totally umbilical submanifold of a Finsler manifold is introduced. Some Gauss equations are given and some results on totally umbilical submanifolds of Riemannian manifolds are generalized. Totally umbilical submanifolds of Randers spaces are studied; a rigidity theorem and an example are given.

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