类 Sasaki 统计空间形式中统计子流形的挤压定理
Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms.
作者信息
Alkhaldi Ali H, Aquib Mohd, Siddiqui Aliya Naaz, Shahid Mohammad Hasan
机构信息
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 62529, Saudi Arabia.
Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, India.
出版信息
Entropy (Basel). 2018 Sep 11;20(9):690. doi: 10.3390/e20090690.
In this paper, we obtain the upper bounds for the normalized δ -Casorati curvatures and generalized normalized δ -Casorati curvatures for statistical submanifolds in Sasaki-like statistical manifolds with constant curvature. Further, we discuss the equality case of the inequalities. Moreover, we give the necessary and sufficient condition for a Sasaki-like statistical manifold to be η -Einstein. Finally, we provide the condition under which the metric of Sasaki-like statistical manifolds with constant curvature is a solution of vacuum Einstein field equations.
在本文中，我们得到了具有常曲率的类 Sasaki 统计流形中统计子流形的归一化 δ - 卡索拉蒂曲率和广义归一化 δ - 卡索拉蒂曲率的上界。此外，我们讨论了不等式的等式情形。而且，我们给出了类 Sasaki 统计流形为 η - 爱因斯坦流形的充分必要条件。最后，我们给出了具有常曲率的类 Sasaki 统计流形的度量是真空爱因斯坦场方程解的条件。
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