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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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.
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