Geometric Analysis of η-Ricci Bourguignon Solitons on Para-Sasakian Manifolds With Semisymmetric Nonmetric Connection (SSNMC) on the Tangent Bundle

Lalnunenga Colney, Dalal Alhwikem, Teg Alam and Anowar Hussain Sadiyal

Journal of Mathematics, 2026, vol. 2026, 1-15

Abstract: In this paper, we investigate the geometric properties of η-Ricci–Bourguignon (η-RB) solitons on para-Sasakian manifolds equipped with a semisymmetric nonmetric connection (SSNMC). By employing the complete lift on the tangent bundle, we derive curvature relations, Ricci identities, Ricci flow, and the corresponding η-RB soliton equations for the lifted manifold. It is shown that the complete lift of an η-RB soliton on a para-Sasakian manifold with SSNMC results in a generalized η-Einstein manifold. The nature of the soliton, such as shrinking, steady, or expanding, is characterized by the sign of the effective soliton coefficient α=λ+βr˜c−1/2. Furthermore, the conditions for Tθ-flat and Tθ–Ricci semisymmetric cases are established, illustrating how specific curvature constraints affect soliton behavior. An explicit example of a five-dimensional para-Sasakian manifold is constructed to verify the theoretical results using partial differential equations (PDEs). These findings extend the framework of η-RB solitons to manifolds with nonmetric connections and provide a foundation for future studies on geometric flows and higher-order lift structures.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1952232

DOI: 10.1155/jom/1952232

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