Alexander A. Ermolitski. Deformations of tensor structures on tagent bundles. Riemannian, Kaehlerian, and hyperkaehlerian manifolds in differential geometry.
Natural Sciences / Mathematics / Geometry
Submitted on: Jun 04, 2012, 03:28:53
Description: Tubular neighborhoods play an important role in differential topology. We have applied these constructions to geometry of almost Hermitian manifolds. At first, we consider deformations of tensor structures on a normal tubular neighborhood of a submanifold in a Riemannian manifold.Further, an almost hyperHermitian structure has been constructed on the tangent bundle TM with help of the Riemannian connection of an almost Hermitian structure on a manifold M then, we consider an embedding of the almost Hermitian manifold M in the corresponding normal tubular neighborhood of the null section in the tangent bundle TM equipped with the deformed almost hyperHermitian structure of the special form. As a result,we have obtained that any smooth manifold M of dimension n can be embedded as a totally geodesic submanifold in a Kaehlerian manifold of dimension 2n and in a hyperKaehlerian manifold of dimension 4n.
The full-text article has been published in the "IntellectualArchive" journal , Vol.1, Num.2, June 2012, ISSN 1929-4700.