Embeddings of almost Hermitian manifolds in almost hyperHermitian those. Complex and hypercomplex numbers in differential geometry
| dc.creator | Ermolitski, Alexander A. | |
| dc.date | 2009-04-23 | |
| dc.date.accessioned | 2026-07-07T13:07:52Z | |
| dc.date.available | 2026-07-07T13:07:52Z | |
| dc.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. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0904.3622 | |
| dc.identifier | http://arxiv.org/abs/0904.3622 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228237 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C15, 53C26, 53C21 | |
| dc.title | Embeddings of almost Hermitian manifolds in almost hyperHermitian those. Complex and hypercomplex numbers in differential geometry | |
| dc.type | text |