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Degenerate Multilinear Forms and Hermitian and Para-Hermitian Structures

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Abstract

We describe some method for obtaining families of complex and paracomplex structures on real manifolds by using degenerate skew-symmetric multilinear forms. To construct these structures, we employ a skew-symmetric form with nontrivial radical and obtain a family of almost complex structures on the six-dimensional sphere different from the Cayley structure and families of Hermitian and para-Hermitian structures on some six-dimensional manifolds.

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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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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 3, pp. 562–578. https://doi.org/10.33048/smzh.2023.64.309

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Kornev, E.S. Degenerate Multilinear Forms and Hermitian and Para-Hermitian Structures. Sib Math J 64, 611–623 (2023). https://doi.org/10.1134/S0037446623030096

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  • DOI: https://doi.org/10.1134/S0037446623030096

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