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Curvature identities for principle T 1-bundles over almost Hermitian manifolds

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Abstract

We show that the identities R 1, R 2 and R 3 for an almost Hermitian structure S on the base of the canonical principal T 1-bundle are equivalent to their contact analogs for the induced almost contact metric structure S # on the total space of this bundle. We prove that the canonical connection of the canonical principal T 1-bundle over a Hermitian or a quasi-Kähler manifold of class R 3 is normal. We also prove that that the canonical connection of the canonical principal T 1-bundle over a Vaisman-Gray manifold M of class R 3 is normal if and only if the Lee vector of M belongs to the center of the adjoint K-algebra.

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Authors and Affiliations

  1. Moscow Pedagogical State University, ul. M. Pirogovskaya 1, Moscow, 119992, Russia

    E. E. Ditkovskaya

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  1. E. E. Ditkovskaya
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Correspondence to E. E. Ditkovskaya.

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Original Russian Text © E.E. Ditkovskaya, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 7, pp. 56–63.

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Ditkovskaya, E.E. Curvature identities for principle T 1-bundles over almost Hermitian manifolds. Russ Math. 54, 49–55 (2010). https://doi.org/10.3103/S1066369X10070054

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  • DOI: https://doi.org/10.3103/S1066369X10070054

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