Praveena, M., Bagewadi, C. (2016). Eisenhart Problem to Submanifolds in Non-Flat Real Space Form. Khayyam Journal of Mathematics, 2(2), 188-193. doi: 10.22034/kjm.2017.42295
Mundalamane Manjappa Praveena; Channabasappa Shanthappa Bagewadi. "Eisenhart Problem to Submanifolds in Non-Flat Real Space Form". Khayyam Journal of Mathematics, 2, 2, 2016, 188-193. doi: 10.22034/kjm.2017.42295
Praveena, M., Bagewadi, C. (2016). 'Eisenhart Problem to Submanifolds in Non-Flat Real Space Form', Khayyam Journal of Mathematics, 2(2), pp. 188-193. doi: 10.22034/kjm.2017.42295
Praveena, M., Bagewadi, C. Eisenhart Problem to Submanifolds in Non-Flat Real Space Form. Khayyam Journal of Mathematics, 2016; 2(2): 188-193. doi: 10.22034/kjm.2017.42295
Eisenhart Problem to Submanifolds in Non-Flat Real Space Form
Department of Mathematics, Kuvempu University, Shankaraghatta - 577 451, Shimoga, Karnataka, India.
Abstract
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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