Conformal nullity of isotropic submanifolds

Volume 86 / 2005

Vladimir Rovenski 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.

Authors

  • Vladimir RovenskiDepartment of Mathematics
    Faculty of Science and Science Education
    University of Haifa
    Mount Carmel, Haifa, 31905 Israel
    e-mail

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