Complexes of differential forms associated with a normalized manifold over the algebra of dual numbers
- Autores: Malyugina A.1, Shurygin V.1
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Afiliações:
- N.I. Lobachevskii Institute of Mathematics and Mechanics
- Edição: Volume 37, Nº 1 (2016)
- Páginas: 66-74
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/197318
- DOI: https://doi.org/10.1134/S1995080216010066
- ID: 197318
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Resumo
We construct some complexes of differential forms on a smooth manifold MnD over the algebra of dual numbers D on the base of a decomposition of the tensor product TMnD⊗ℝD 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 TMnD. For holomorphic fiber bundles over MnD, 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.
Sobre autores
A. Malyugina
N.I. Lobachevskii Institute of Mathematics and Mechanics
Autor responsável pela correspondência
Email: alexandra.malyugina@gmail.com
Rússia, Kremlevskaya str. 18, Kazan, 420008
V. Shurygin
N.I. Lobachevskii Institute of Mathematics and Mechanics
Email: alexandra.malyugina@gmail.com
Rússia, Kremlevskaya str. 18, Kazan, 420008