Conformal nullity of isotropic submanifolds
Volume 86 / 2005
Annales Polonici Mathematici 86 (2005), 47-57
MSC: Primary 53B25, 53C40.
DOI: 10.4064/ap86-1-6
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.
