@article {
author = {Praveena, Mundalamane Manjappa and Bagewadi, Channabasappa Shanthappa},
title = {Eisenhart Problem to Submanifolds in Non-Flat Real Space Form},
journal = {Khayyam Journal of Mathematics},
volume = {2},
number = {2},
pages = {188-193},
year = {2016},
publisher = {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)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2017.42295},
abstract = {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.},
keywords = {Real space forms,submanifolds,parallel second order covariant tensor field,recurrent},
url = {http://www.kjm-math.org/article_42295.html},
eprint = {http://www.kjm-math.org/article_42295_b3ab5c2748d3801e75a0a1f541fa98b0.pdf}
}