TY - JOUR
ID - 42295
TI - Eisenhart Problem to Submanifolds in Non-Flat Real Space Form
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Praveena, Mundalamane Manjappa
AU - Bagewadi, Channabasappa Shanthappa
AD - Department of Mathematics, Kuvempu University, Shankaraghatta - 577 451,
Shimoga, Karnataka, India.
Y1 - 2016
PY - 2016
VL - 2
IS - 2
SP - 188
EP - 193
KW - Real space forms
KW - submanifolds
KW - parallel second order covariant tensor field
KW - recurrent
DO - 10.22034/kjm.2017.42295
N2 - 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.
UR - http://www.kjm-math.org/article_42295.html
L1 - http://www.kjm-math.org/article_42295_b3ab5c2748d3801e75a0a1f541fa98b0.pdf
ER -