Extrinsic geometry of parabolic and saddle multidimensional manifolds

Abstract

Contents Introduction § 1. Parabolic submanifolds 1.1. Point structure of the space of second fundamental forms of a k-parabolic surface 1.2. Normal bundle of a manifold 1.3. Local structure of the k-parabolic submanifolds in a Riemannian space 1.4. Complete parabolic submanifolds of a Riemannian space 1.5. Pontryagin characteristic classes of parabolic submanifolds in a spherical space § 2. k-saddle and k-convex submanifolds 2.1. Topological structure of saddle submanifolds 2.2. Intersection of saddle submanifolds in a Riemannian space 2.3. k-asymptotic and k-convex submanifolds § 3. Submanifolds of non-positive extrinsic curvature 3.1. Extrinsic curvature 3.2. Foliations on Riemannian manifolds 3.3. Affinely stable immersions of Riemannian metricsBibliography