Об обобщенных многообразиях Кенмоцу как гиперповерхностях многообразий Вайсмана - Грея

Y.A. Mohammed
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Abstract

In this paper, we conclude that the hypersurfaces of Vaisman-Gray manifolds have generalized Kenmotsu structures under some conditions for the Lee form, Kirichenko's tensors and the second fundamental form of the immersion of the hypersurface into the manifold of Vaisman-Gray class. Moreover, the components of the second fundamental form are determined when the foregoing hypersurfaces have generalized Kenmotsu structures or any special kind of it or Kenmotsu structures, such that some of these components are vanish. Also, some components of Lee form and some components of some Kirichenko's tensors in the Vaisman--Gray class are equal to zero. On the other hand, the minimality of totally umbilical, totally geodesic hypersurfaces of Vaisman--Gray manifolds with generalized Kenmotsu structures are investigated. In addition, we deduced that the hypersurface of Vaisman--Gray manifold that have generalized Kenmotsu structure is totally geodesic if and only if it is totally umbilical and some components of Lee form are constants.
论作为魏斯曼-格雷流形超曲面的广义肯莫特流形
在本文中,我们得出结论,在李形式、基里琴科张量和超曲面浸入 Vaisman-Gray 类流形的第二基本形式的某些条件下,Vaisman-Gray 流形的超曲面具有广义 Kenmotsu 结构。此外,当前述超曲面具有广义 Kenmotsu 结构或它或 Kenmotsu 结构的任何特殊类型时,第二基本形式的分量是确定的,这样其中一些分量就会消失。此外,在维斯曼-格雷类中,李形式的某些分量和某些基里琴科张量的某些分量等于零。另一方面,我们研究了具有广义肯莫津结构的维斯曼-格雷流形的全脐、全测地超曲面的最小性。此外,我们还推导出,当且仅当具有广义 Kenmotsu 结构的 Vaisman-Gray 流形的超曲面是全全大地曲面且李形式的某些分量是常数时,它才是全全大地曲面。
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