extrinsic sphere and totally umbilical submanifolds in finsler spaces
نویسندگان
چکیده
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.
منابع مشابه
Extrinsic sphere and totally umbilical submanifolds in Finsler spaces
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...
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عنوان ژورنال:
bulletin of the iranian mathematical societyجلد ۴۳، شماره ۲، صفحات ۳۳۷-۳۴۷
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