Abstract
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.
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Original Russian Text Copyright © 2014 Kornev E.S.
The author was supported by the Russian Foundation for Basic Research (Grant 12-01-00873-a) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-544.2012.1).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 6, pp. 1283–1296, November–December, 2014.
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Kornev, E.S. Affinor structures on vector bundles. Sib Math J 55, 1045–1055 (2014). https://doi.org/10.1134/S003744661406007X
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DOI: https://doi.org/10.1134/S003744661406007X