Masaltsev L. Geometry of multidimensional submanifolds of homogeneous Riemannian spaces

Objects: submanifolds of homogeneous Riemannian spaces. Goals: to prove definite properties of external geometry of submanifolds in homogeneous Riemannian spaces. Methods: methods of differential and Riemannian geometry, theory of differential equations, theory of harmonic mappings of Riemannian manifolds. New theoretical results: the problem of isometric immersion of homogeneous geometries Nil, SL2, Sol into four-dimensional space of constant curvature is solved, minimal ruled surfaces in homogeneous geometries are found, theorems about harmonicity of Gaussian map in Lobachevskiy space and spherical space are proved. Employment: The results are important for applications in theory of isometric immersions of manifolds, theory of minimal submanifolds in Riemannian spaces, theory of harmonic mappings of Riemannian manifolds.