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

Year 2022, Volume: 15 Issue: 2, 277 - 286, 31.10.2022

Aliya Naaz Sıddıquı , Siraj Uddin , Mohammad Hasan Shahid

https://doi.org/10.36890/iejg.1006287

Cited By: 4

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

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