Savyel'yev V. Theory curvature of the Grassmannian image of submanifolds in Euclidean and Riemannian spaces

Object of research: sectional curvature of the Grassmann manifold in the tangent planes of the Grassmannian image submanifolds in Euclidean space.Goal of research: the proof of Borysenko's hypothesys,proof of the theorems on the curvature of the Grassmannian image.Methods of research: methods of local differential geometry, linear algebra. New theoretical results:Borysenko's theorem is proved for many cases, the formula for curvatures connecting with Grassmannian image is obtained on the basis of the systematic usage of the theory of curvature of Grassmannian image to study geometrical properties of submanifolds in Euclidean space.