Bounds for Statistical Curvatures of Submanifolds in Kenmotsu-like Statistical Manifolds

Aliya Naaz Siddiqui, Mohd Danish Siddiqi and Ali Hussain Alkhaldi
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Aliya Naaz Siddiqui: Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala 133207, India
Mohd Danish Siddiqi: Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
Ali Hussain Alkhaldi: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia

Mathematics, 2022, vol. 10, issue 2, 1-15

Abstract: In this article, we obtain certain bounds for statistical curvatures of submanifolds with any codimension of Kenmotsu-like statistical manifolds. In this context, we construct a class of optimum inequalities for submanifolds in Kenmotsu-like statistical manifolds containing the normalized scalar curvature and the generalized normalized Casorati curvatures. We also define the second fundamental form of those submanifolds that satisfy the equality condition. On Legendrian submanifolds of Kenmotsu-like statistical manifolds, we discuss a conjecture for Wintgen inequality. At the end, some immediate geometric consequences are stated.

Keywords: statistical manifolds; kenmotsu-like statistical manifolds; casorati curvatures; generalized wintgen inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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