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2021 Hypersurfaces of the nearly Kähler twistor spaces $\mathbb{C}\mathrm{P}^3$ and ${\mathbb{F}_{1,2}}$
Guillaume Deschamps, Eric Loubeau
Tohoku Math. J. (2) 73(4): 627-642 (2021). DOI: 10.2748/tmj.20200930

Abstract

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

Citation

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Guillaume Deschamps. Eric Loubeau. "Hypersurfaces of the nearly Kähler twistor spaces $\mathbb{C}\mathrm{P}^3$ and ${\mathbb{F}_{1,2}}$." Tohoku Math. J. (2) 73 (4) 627 - 642, 2021. https://doi.org/10.2748/tmj.20200930

Information

Published: 2021
First available in Project Euclid: 22 December 2021

Digital Object Identifier: 10.2748/tmj.20200930

Subjects:
Primary: 32L25
Secondary: 53C15 , 53C28 , 53C55

Rights: Copyright © 2021 Tohoku University

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Vol.73 • No. 4 • 2021
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