Affinor structures on vector bundles

An affinor structure is a generalization of the notion of an almost complex structure associated with a symplectic form on a manifold of even dimension for vector bundles of arbitrary rank. An affinor structure is the field of the automorphisms of the vector bundle preserving the exterior derivative...

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Bibliographic Details
Published in:Siberian mathematical journal 2014-11, Vol.55 (6), p.1045-1055
Main Author: Kornev, E. S.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:An affinor structure is a generalization of the notion of an almost complex structure associated with a symplectic form on a manifold of even dimension for vector bundles of arbitrary rank. An affinor structure is the field of the automorphisms of the vector bundle preserving the exterior derivative of some 1-form with radical of arbitrary dimension. The exterior derivative can be always defined on Lie algebroids, a special class of vector bundles. Therefore, the theory of affinor structures is considered on Lie algebroids. We show that the classical objects, such as a symplectic structure, a contact structure, and a Kähler structure, are particular cases of the general theory of affinor metric structures.
ISSN:0037-4466
1573-9260
DOI:10.1134/S003744661406007X