Sharief Deshmukh
Abstract
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In this Note, we show that the presence of a unit Killing vector field ξ on an orientable compact hypersurface of a Euclidean space with shape operator A and induced metric g such that g ( A ξ , ξ ) is a constant, renders it to be a round sphere and also influences the dimension of the ambient Euclidean space.
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In this Note, we show that the presence of a unit Killing vector field ξ on an orientable compact hypersurface of a Euclidean space with shape operator A and induced metric g such that g ( A ξ , ξ ) is a constant, renders it to be a round sphere and also influences the dimension of the ambient Euclidean space.
Key concepts: Hypersurface, Mathematics, Euclidean space, Euclidean geometry, Unit sphere, Vector field, Constant (computer programming), Pure mathematics