تقرير
On Hopf hypersurfaces of the homogeneous nearly K\'ahler $\mathbf{S}^3\times\mathbf{S}^3$
| العنوان: | On Hopf hypersurfaces of the homogeneous nearly K\'ahler $\mathbf{S}^3\times\mathbf{S}^3$ |
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| المؤلفون: | Hu, Zejun, Yao, Zeke |
| المصدر: | Annali di Matematica Pura ed Applicata (1923 -) 199 (2020),1147-1170 |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, 53B25, 53B35, 53C30, 53C42 |
| الوصف: | In this paper, extending our previous joint work (Hu et al., Math Nachr 291:343--373, 2018), we initiate the study of Hopf hypersurfaces in the homogeneous NK (nearly K\"ahler) manifold $\mathbf{S}^3\times\mathbf{S}^3$. First, we show that any Hopf hypersurface of the homogeneous NK $\mathbf{S}^3\times\mathbf{S}^3$ does not admit two distinct principal curvatures. Then, for the important class of Hopf hypersurfaces with three distinct principal curvatures, we establish a complete classification under the additional condition that their holomorphic distributions $\{U\}^\perp$ are preserved by the almost product structure $P$ of the homogeneous NK $\mathbf{S}^3\times\mathbf{S}^3$. Comment: 26 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s10231-019-00915-z |
| URL الوصول: | http://arxiv.org/abs/1904.09638 |
| رقم الأكسشن: | edsarx.1904.09638 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s10231-019-00915-z |
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