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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 Kahler) manifold $mathbf{S}^3timesmathbf{S}^3$. First, we show that any Hopf hypersurface of the homogeneous NK $mathbf{S}^3timesmathbf{S}^3$ 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 $mathbf{S}^3timesmathbf{S}^3$.
Each hypersurface of a nearly Kahler 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 NK $mathbb{S}^6$
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 mani
We prove that a 2n-dimensional compact homogeneous nearly Kahler manifold with strictly positive sectional curvature is isometric to CP^{n}, equipped with the symmetric Fubini-Study metric or with the standard Sp(m)-homogeneous metric, n =2m-1, or to
The moduli space NK of infinitesimal deformations of a nearly Kahler structure on a compact 6-dimensional manifold is described by a certain eigenspace of the Laplace operator acting on co-closed primitive (1,1) forms. Using the Hermitian Laplace ope
We find a class of minimal hypersurfaces H(k) as the zero level set of Pfaffians, resp. determinants of real 2k+2 dimensional antisymmetric matrices. While H(1) and H(2) are congruent to a 6-dimensional quadratic cone resp. Hsiangs cubic su(4) invari