Displaying similar documents to “On totally umbilical submanifolds of a locally Minkowski manifold.”

Cauchy-Riemann submanifolds of Kaehlerian Finsler spaces.

Sorin Dragomir (1989)

Collectanea Mathematica

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We study the geometry of the second fundamental form of a Cauchy-Riemann submanifold of a Kaehlerian Finsler space M2n; any totally-real submanifold of M2n with v-flat normal connection is shown to be a Berwald-Cartan space.

Volume comparison theorem for tubular neighborhoods of submanifolds in Finsler geometry and its applications

Bing-Ye Wu (2014)

Annales Polonici Mathematici

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We consider the distance to compact submanifolds and study volume comparison for tubular neighborhoods of compact submanifolds. As applications, we obtain a lower bound for the length of a closed geodesic of a compact Finsler manifold. When the Finsler metric is reversible, we also provide a lower bound of the injectivity radius. Our results are Finsler versions of Heintze-Karcher's and Cheeger's results for Riemannian manifolds.

On totally umbilical submanifolds of Finsler spaces

Qun He, Wei Yang, Wei Zhao (2011)

Annales Polonici Mathematici

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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.

Doubly warped product Finsler manifolds with some non-Riemannian curvature properties

Esmaeil Peyghan, Akbar Tayebi, Behzad Najafi (2012)

Annales Polonici Mathematici

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We consider doubly warped product (DWP) Finsler manifolds with some non-Riemannian curvature properties. First, we study Berwald and isotropic mean Berwald DWP-Finsler manifolds. Then we prove that every proper Douglas DWP-Finsler manifold is Riemannian. We show that a proper DWP-manifold is Landsbergian if and only if it is Berwaldian. Then we prove that every relatively isotropic Landsberg DWP-manifold is a Landsberg manifold. We show that a relatively isotropic mean Landsberg warped...