Eisenhart Problem to Submanifolds in Non-Flat Real Space Form

Document Type : Original Article


Department of Mathematics, Kuvempu University, Shankaraghatta - 577 451, Shimoga, Karnataka, India.


We apply the Eisenhart problem to study the geometric properties of
submanifold $M$ 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.


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