Extrinsic geometry of strongly parabolic multidimensional submanifolds

Abstract

Contents §1. Introduction §2. Affine classification of points of multidimensional surfaces 2.1. Main results 2.2. Proof of Theorem 2.1.1 2.3. Classification of points of 3-dimensional submanifolds §3. Strongly parabolic submanifolds 3.1. Local structure of a strongly parabolic surface in Riemannian space 3.2. Local structure of a strongly parabolic surface in Euclidean space 3.3. Complete strongly parabolic multidimensional surfaces in Euclidean space 3.4. Conditions under which complete strongly parabolic submanifolds in spherical space are totally geodesic 3.5. Strongly parabolic submanifolds in Lobachevskii space 3.6. Strongly parabolic submanifolds in pseudo-Euclidean and pseudo-Riemannian spaces of constant curvature 3.7. Strongly parabolic submanifolds and minimal surfacesBibliography