Extrinsic sphere and totally umbilical submanifolds in Finsler spaces

Document Type : Research Paper


Faculty of‎ ‎Mathematics and Computer Science‎, ‎Amirkabir University of Technology (Tehran Polytechnic)‎, ‎15914‎, ‎Tehran‎, ‎Iran.


‎Based on a definition for circle in Finsler space‎, ‎recently proposed by one of the present authors and Z‎. ‎Shen‎, ‎a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient manifold‎.
Finally‎, ‎some examples of extrinsic sphere in Finsler geometry‎, ‎particularly in Randers spaces are given.


Main Subjects

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