Conformal nullity of isotropic submanifolds

Vladimir Rovenski. "Conformal nullity of isotropic submanifolds." Annales Polonici Mathematici 86.1 (2005): 47-57. <http://eudml.org/doc/280168>.

@article{VladimirRovenski2005,
abstract = {We introduce and study submanifolds with extrinsic curvature and second fundamental form related by an inequality that holds for isotropic submanifolds and becomes equality for totally umbilical submanifolds. The dimension of umbilical subspaces and the index of conformal nullity of these submanifolds with low codimension are estimated from below. The corollaries are characterizations of extrinsic spheres in Riemannian spaces of positive curvature.},
author = {Vladimir Rovenski},
journal = {Annales Polonici Mathematici},
keywords = {submanifold; isotropic; totally umbilical; extrinsic curvature; conformal nullity},
language = {eng},
number = {1},
pages = {47-57},
title = {Conformal nullity of isotropic submanifolds},
url = {http://eudml.org/doc/280168},
volume = {86},
year = {2005},
}

TY - JOUR
AU - Vladimir Rovenski
TI - Conformal nullity of isotropic submanifolds
JO - Annales Polonici Mathematici
PY - 2005
VL - 86
IS - 1
SP - 47
EP - 57
AB - We introduce and study submanifolds with extrinsic curvature and second fundamental form related by an inequality that holds for isotropic submanifolds and becomes equality for totally umbilical submanifolds. The dimension of umbilical subspaces and the index of conformal nullity of these submanifolds with low codimension are estimated from below. The corollaries are characterizations of extrinsic spheres in Riemannian spaces of positive curvature.
LA - eng
KW - submanifold; isotropic; totally umbilical; extrinsic curvature; conformal nullity
UR - http://eudml.org/doc/280168
ER -