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Subcomplex and sub-Kähler structures

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Abstract

We introduce the notion of subcomplex structure on a manifold of arbitrary real dimension and consider some important particular cases of pseudocomplex structures: pseudotwistor, affinor, and sub-Kähler structures. It is shown how subtwistor and affinor structures can give sub-Riemannian and sub-Kähler structures. We also prove that all classical structures (twistor, Kähler, and almost contact metric structures) are particular cases of subcomplex structures. The theory is based on the use of a degenerate 1-form or a 2-form with radical of arbitrary dimension.

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Authors and Affiliations

  1. Kemerovo State University, Kemerovo, Russia

    E. S. Kornev

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  1. E. S. Kornev
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Correspondence to E. S. Kornev.

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Kemerovo. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 5, pp. 1062–1077, September–October, 2016; DOI: 10.17377/smzh.2016.57.512.

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Kornev, E.S. Subcomplex and sub-Kähler structures. Sib Math J 57, 830–840 (2016). https://doi.org/10.1134/S0037446616050128

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  • DOI: https://doi.org/10.1134/S0037446616050128

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