Conformal nullity of isotropic submanifolds

• Autorzy: Vladimir Rovenski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53B25: Local submanifolds
• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2005
• Tom: 86
• Numer: 1
• Strony: 47-57

Daty

wydano

2005

Twórcy

autor

Vladimir Rovenski

• Department of Mathematics, Faculty of Science and Science Education, University of Haifa, Mount Carmel, Haifa, 31905 Israel

Identyfikatory

DOI

10.4064/ap86-1-6