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arXiv · 1912.08000

Hypersurfaces of nearly Kahler twistor spaces

G. Deschamps·E. Loubeau
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Abstract

In this article, we show that a hypersurface of the nearly Kahler $CP^3$ or $F_{1,2}$ cannot have its shape operator and induced almost contact structure commute together. This settles the question for six-dimensional homogeneous nearly Kahler manifolds, as the cases of $S^6$ and $S^3 \times S^3$ were previously solved, and provides a counterpart to the more classical question for the complex space forms $CP^n$ and $CH^n$. The proof relies heavily on the construction of $CP^3$ and $F_{1,2}$ as twistor spaces of $S^4$ and $CP^2$

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G. Deschamps, E. Loubeau. 2019-12-17. Hypersurfaces of nearly Kahler twistor spaces. https://arxiv.org/abs/1912.08000

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