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Open AccessArticle

Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms

1
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 62529, Saudi Arabia
2
Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, India
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2018, 20(9), 690; https://doi.org/10.3390/e20090690
Received: 12 August 2018 / Revised: 5 September 2018 / Accepted: 7 September 2018 / Published: 11 September 2018
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. View Full-Text
Keywords: Casorati curvatures; statistical manifolds; Sasaki-like statistical space forms; η-Einstein Casorati curvatures; statistical manifolds; Sasaki-like statistical space forms; η-Einstein
MDPI and ACS Style

Alkhaldi, A.H.; Aquib, M.; Siddiqui, A.N.; Shahid, M.H. Pinching Theorems for Statistical Submanifolds in Sasaki-Like Statistical Space Forms. Entropy 2018, 20, 690.

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