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.
Keywords:subcomplex structure, affinor structure, sub-Kähler structure, radical of a multilinear form.
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