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)Khayyam Journal of Mathematics2423-47882220160801Eisenhart Problem to Submanifolds in Non-Flat Real Space Form1881934229510.22034/kjm.2017.42295ENMundalamane ManjappaPraveenaDepartment of Mathematics, Kuvempu University, Shankaraghatta - 577 451,
Shimoga, Karnataka, India.Channabasappa ShanthappaBagewadiDepartment of Mathematics, Kuvempu University, Shankaraghatta - 577 451,
Shimoga, Karnataka, India.Journal Article20161019We apply the Eisenhart problem to study the geometric properties of<br />submanifold $M$ of non-flat real space form. It is shown that $M$<br /> is a hypersphere $S^{3}$ when $\sigma$ is parallel. When $\sigma$ is either semi-parallel or recurrent,<br /> then $M$ is either an extrinsic sphere and normal flat or mean curvature vector is parallel in the normal space, respectively.http://www.kjm-math.org/article_42295_b3ab5c2748d3801e75a0a1f541fa98b0.pdf