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Twistorial construction of minimal hypersurfaces

Johann Davidov

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, Bulgaria

"L. Karavelov" Civil Engineering Higher School, 1373 Sofia, Bulgaria

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https://doi.org/10.1142/S0219887814500649Cited by:5 (Source: Crossref)

Abstract

Every almost Hermitian structure (g, J) on a four-manifold M determines a hypersurface Σ_J in the (positive) twistor space of (M, g) consisting of the complex structures anti-commuting with J. In this paper, we find the conditions under which Σ_J is minimal with respect to a natural Riemannian metric on the twistor space in the cases when J is integrable or symplectic. Several examples illustrating the obtained results are also discussed.

Keywords:

AMSC: Primary 53C28, Secondary 53A10, Secondary 49Q05

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