B.-Y. Chen`s Inequality for Kähler-like Statistical Submersions

Authors : Aliya Naaz SIDDIQUI, Siraj UDDİN, Mohammad Hasan SHAHİD

Pages : 277-286

Doi:10.36890/iejg.1006287

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Publication Date : 2022-10-31

Article Type : Research Paper

Abstract :In this paper, we first define the notion of Lagrangian statistical submersion from a K\`ahler-like statistical manifold onto a statistical manifold. Then we prove that the horizontal distribution of a Lagrangian statistical submersion is integrable. Next, we establish Chen-Ricci inequality for Lagrangian statistical submersions from K\`ahler-like statistical manifolds onto statistical manifolds and discuss the equality case of the obtained inequality through a basic tensor introduced by O`Neill that plays the role of the second fundamental form of an isometric immersion. At the end, we give a nontrivial example of a K\`ahler-like statistical submersion.
Keywords : Statistical submersions, Lagrangian statistical submersions, Kähler like statistical submersions, statistical manifolds, Chen Ricci Inequality