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Please use this identifier to cite or link to this item: https://libeldoc.bsuir.by/handle/123456789/10436
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dc.contributor.authorErmolitski, A. A.-
dc.date.accessioned2016-11-29T10:59:20Z-
dc.date.accessioned2017-07-27T12:26:56Z-
dc.date.available2016-11-29T10:59:20Z-
dc.date.available2017-07-27T12:26:56Z-
dc.date.issued2014-
dc.identifier.citationErmolitski, A. A. Embeddings of Almost Hermitian Manifold in Almost Hyper Hermitian Manifold and Complex (Hypercomplex) Numbers in Riemannian Geometry / A. A. Ermolitski // Applied Mathematics. - 2014 . - № 5. - P. 2464 - 2475.ru_RU
dc.identifier.urihttps://libeldoc.bsuir.by/handle/123456789/10436-
dc.description.abstractTubular 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 hyper Hermitian 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 hyper Hermitian structure of the special form. As a result, we have obtained that any Riemannian manifold M of dimension n can be embedded as a totally geodesic submanifold in a Kaehlerian manifold of dimension 2n (Theorem 6) and in a hyper Kaehlerian manifold of dimension 4n (Theorem 7). Such embeddings are “good” from the point of view of Riemannian geometry. They allow solving problems of Riemannian geometry by methods of Kaehlerian geometry (see Section 5 as an example). We can find similar situation in mathematical analysis (real and complex).ru_RU
dc.language.isoenru_RU
dc.publisherCreative Commons Attribution International License (CC BY).ru_RU
dc.subjectпубликации ученыхru_RU
dc.subjectRiemannian Manifolds-
dc.subjectAlmost Hermitian and Almost Hyper Hermitian Structures-
dc.titleEmbeddings of Almost Hermitian Manifold in Almost Hyper Hermitian Manifold and Complex (Hypercomplex) Numbers in Riemannian Geometryru_RU
dc.typeArticleru_RU
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