Quaternion Statistical Submanifolds and Submersions

Aliya Naaz Siddiqui and Fatimah Alghamdi ()
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Aliya Naaz Siddiqui: Division of Mathematics, School of Basic Sciences, Galgotias University, Greater Noida 203201, Uttar Pradesh, India
Fatimah Alghamdi: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia

Mathematics, 2024, vol. 13, issue 1, 1-18

Abstract: This paper aims to develop a general theory of quaternion Kahlerian statistical manifolds and to study quaternion CR-statistical submanifolds in such ambient manifolds. It extends the existing theories of quaternion submanifolds and totally real submanifolds. Additionally, the work examines quaternion Kahlerian statistical submersions, including illustrative examples. The exploration also includes an analysis of the total space and fibers under certain conditions with example(s) in support. Moreover, Chen–Ricci inequality on the vertical distribution is derived for quaternion Kahlerian statistical submersions from quaternion Kahlerian statistical manifolds.

Keywords: statistical manifolds; quaternion Kahlerian statistical manifolds; Lagrangian submanifolds; quaternion CR-statistical submanifolds; statistical submersions; quaternion Kahlerian statistical submersions; Chen–Ricci inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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