%0 Journal Article
%T Eisenhart Problem to Submanifolds in Non-Flat Real Space Form
%J Khayyam Journal of Mathematics
%I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
%Z 2423-4788
%A Praveena, Mundalamane Manjappa
%A Bagewadi, Channabasappa Shanthappa
%D 2016
%\ 08/01/2016
%V 2
%N 2
%P 188-193
%! Eisenhart Problem to Submanifolds in Non-Flat Real Space Form
%K Real space forms
%K submanifolds
%K parallel second order covariant tensor field
%K recurrent
%R 10.22034/kjm.2017.42295
%X We apply the Eisenhart problem to study the geometric properties ofsubmanifold $M$ of non-flat real space form. It is shown that $M$ is a hypersphere $S^{3}$ when $\sigma$ is parallel. When $\sigma$ is either semi-parallel or recurrent, then $M$ is either an extrinsic sphere and normal flat or mean curvature vector is parallel in the normal space, respectively.
%U http://www.kjm-math.org/article_42295_b3ab5c2748d3801e75a0a1f541fa98b0.pdf