KFU. Card publication. Complexes of differential forms associated with a normalized manifold over the algebra of dual numbers

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COMPLEXES OF DIFFERENTIAL FORMS ASSOCIATED WITH A NORMALIZED MANIFOLD OVER THE ALGEBRA OF DUAL NUMBERS

Form of presentation

Articles in international journals and collections

Year of publication

2016

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Authors, employees of KFU

Shurygin Vadim Vasilevich, author

Bibliographic description in the original language

Malyugina A.A, Shurygin V.V., Complexes of differential forms associated with a normalized manifold over the algebra of dual numbers//Lobachevskii Journal of Mathematics. - 2016. - Vol.37, Is.1. - P.66-74.

Annotation

We construct some complexes of differential forms on a smooth manifold MD^n over the algebra of dual numbers D on the base of a decomposition of the tensor product TMD n ⊗R D into the Whitney sum of two subbundles. It is shown that these complexes can be obtained as restrictions of some complexes of holomorphic (D-smooth) forms defined on the tangent bundle TMDn . For holomorphic fiber bundles over MDn , we introduce complexes of D-valued forms holomorphic along the fibers and express in terms of cohomology classes of such complexes the obstructions to existence of holomorphic connections in holomorphic principal bundles.

Keywords

Almost tangent structure, Atiyah class manifold over the algebra of dual numbers, manifold over Weil algebra, tangent bundle, tangent manifold

The name of the journal

Lobachevskii Journal of Mathematics

URL

http://www.scopus.com/inward/record.url?eid=2-s2.0-84955457820&partnerID=40&md5=7dce52c1970df8a21e93d49ee29bea1e

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=130342&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Shurygin Vadim Vasilevich	ru_RU
dc.date.accessioned	2016-01-01T00:00:00Z	ru_RU
dc.date.available	2016-01-01T00:00:00Z	ru_RU
dc.date.issued	2016	ru_RU
dc.identifier.citation	Malyugina A.A, Shurygin V.V., Complexes of differential forms associated with a normalized manifold over the algebra of dual numbers//Lobachevskii Journal of Mathematics. - 2016. - Vol.37, Is.1. - P.66-74.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=130342&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	We construct some complexes of differential forms on a smooth manifold MD^n over the algebra of dual numbers D on the base of a decomposition of the tensor product TMD n ⊗R D into the Whitney sum of two subbundles. It is shown that these complexes can be obtained as restrictions of some complexes of holomorphic (D-smooth) forms defined on the tangent bundle TMDn . For holomorphic fiber bundles over MDn , we introduce complexes of D-valued forms holomorphic along the fibers and express in terms of cohomology classes of such complexes the obstructions to existence of holomorphic connections in holomorphic principal bundles.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Almost tangent structure	ru_RU
dc.subject	Atiyah class manifold over the algebra of dual numbers	ru_RU
dc.subject	manifold over Weil algebra	ru_RU
dc.subject	tangent bundle	ru_RU
dc.subject	tangent manifold	ru_RU
dc.title	Complexes of differential forms associated with a normalized manifold over the algebra of dual numbers	ru_RU
dc.type	Articles in international journals and collections	ru_RU