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november 2019 Hypersurfaces of the homogeneous nearly Kähler $\mathbb{S}^6$ and $\mathbb{S}^3\times\mathbb{S}^3$ with anticommutative structure tensors
Zejun Hu, Zeke Yao, Xi Zhang
Bull. Belg. Math. Soc. Simon Stevin 26(4): 535-549 (november 2019). DOI: 10.36045/bbms/1576206356

Abstract

Each hypersurface of a nearly Kähler manifold is naturally equipped with two tensor fields of $(1,1)$-type, namely the shape operator $A$ and the induced almost contact structure $\phi$. In this paper, we show that, in the homogeneous nearly Kähler $\mathbb{S}^6$ a hypersurface satisfies the condition $A\phi+\phi A=0$ if and only if it is totally geodesic; moreover, similar as for the non-flat complex space forms, the homogeneous nearly Kähler manifold $\mathbb{S}^3\times\mathbb{S}^3$ does not admit a hypersurface that satisfies the condition $A\phi+\phi A=0$.

Citation

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Zejun Hu. Zeke Yao. Xi Zhang. "Hypersurfaces of the homogeneous nearly Kähler $\mathbb{S}^6$ and $\mathbb{S}^3\times\mathbb{S}^3$ with anticommutative structure tensors." Bull. Belg. Math. Soc. Simon Stevin 26 (4) 535 - 549, november 2019. https://doi.org/10.36045/bbms/1576206356

Information

Published: november 2019
First available in Project Euclid: 13 December 2019

zbMATH: 07167743
MathSciNet: MR4042400
Digital Object Identifier: 10.36045/bbms/1576206356

Subjects:
Primary: 53B35, 53C30, 53C42

Rights: Copyright © 2019 The Belgian Mathematical Society

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Vol.26 • No. 4 • november 2019
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