Extrinsic geometry of multidimensional submanifolds in different ambient spaces: euclidean, spaces of constant curvature, symmetric spaces of rank one, Riemannian and pseudoriemannian spaces. Metric and topological properties.
The Gauss image of submanifolds.
Convex hypersurfaces in Riemannian spaces, in spaces of constant curvature.
Foliations on Riemannian manifolds: saddle, convex, parabolic.
Bundles over Riemannian manifolds: tangent bundle of a Riemannian manifold, normal bundle of a submanifold in Riemannian or pseudoriemannian space.
Global Riemannian geometry of nonpositively curved manifolds.
Geometry Research Group
School of Mathematics and Informatics
Svobody sq., 4, aud. 2-29,
Kharkiv, 61022, Ukraine