- International Electronic Journal of Geometry
- Vol: 15 Issue: 2
- B.-Y. Chen's Inequality for Kähler-like Statistical Submersions
B.-Y. Chen's Inequality for Kähler-like Statistical Submersions
Authors : Aliya Naaz Siddiqui, Siraj Uddin, Mohammad Hasan Shahid
Pages : 277-286
Doi:10.36890/iejg.1006287
View : 6 | Download : 3
Publication Date : 2022-10-31
Article Type : Research
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