Geometry of statistical submanifolds of statistical warped product manifolds by optimization techniques

2019/01/17 by Siddiqui, Aliya Naaz, Mofarreh, Fatemah, Alkhaldi, Ali Hussain +1
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.05625

Abstract

This paper deals with the applications of an optimization method on submanifolds, that is, geometric inequalities can be considered as optimization problems. In this regard, we obtain optimal Casorati inequalities and Chen-Ricci inequality for a statistical submanifold in a statistical warped product manifold of type ℝ ×_\mathfrakf M (almost Kenmotsu statistical manifold), where ℝ and M are trivial statistical manifold and almost Kaehler statistical manifold, respectively.

Related

• Extremities for statistical submanifolds in Kenmotsu statistical\n manifolds
• Basic inequality for statistical submanifolds of quaternion Kaehler-like statistical manifolds
• On CR-statistical submanifolds of holomorphic statistical manifolds
• Chen Inequality for Statistical Submanifolds of Cosymplectic Manifolds
• Locally Product-like Statistical Manifolds and Their Hypersurfaces