Embeddings of almost Hermitian manifolds in almost hyperHermitian those. Complex and hypercomplex numbers in differential geometry

Details Embeddings of almost Hermitian manifolds in almost hyperHermitian those. Complex and hypercomplex numbers in differential geometry Embeddings of almost Hermitian manifolds in almost hyperHermitian those. Complex and hypercomplex numbers in differential geometry

2009-04-23

arxiv.org/abs/0904.3622v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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.

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