Geodesic
Conformal nullity of isotropic submanifolds
Vladimir Rovenski1
1 Department of Mathematics Faculty of Science and Science Education University of Haifa Mount Carmel, Haifa, 31905 Israel
Annales Polonici Mathematici, Tome 86 (2005) no. 1, pp. 47-57 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap86-1-6
Keywords: introduce study submanifolds extrinsic curvature second fundamental form related inequality holds isotropic submanifolds becomes equality totally umbilical submanifolds dimension umbilical subspaces index conformal nullity these submanifolds low codimension estimated below corollaries characterizations extrinsic spheres riemannian spaces positive curvature

Vladimir Rovenski 1

1 Department of Mathematics Faculty of Science and Science Education University of Haifa Mount Carmel, Haifa, 31905 Israel 
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Vladimir Rovenski. Conformal nullity of isotropic submanifolds. Annales Polonici Mathematici, Tome 86 (2005) no. 1, pp. 47-57. doi: 10.4064/ap86-1-6

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