Research Article

Characterizations of *-Ricci-Bourguignon solitons and contact Ricci-Bourguignon almost solitons

Published in: Quaestiones Mathematicae
Volume 48 , issue 9 , 2025 , pages: 1395–1416

DOI: 10.2989/16073606.2025.2505516

Author(s): Sourav Nayak Indian Institute of Technology – Hyderabad, India , Dhriti Sundar Patra Indian Institute of Technology – Hyderabad, India , Hemangi Madhusudan Shah Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute, India

Keywords: 53C25 , 53C21 , 53D15 , *-Ricci-Bourguignon soliton , *-Ricci tensor ,

-homothetically fixed null η-Einstein

, Sasakian manifold , infinitesimal contact transformation , Jacobi field , α-cosymplectic manifold

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Abstract

In this paper, we first study *-Ricci-Bourguignon solitons (in short, *-RB solitons) and find their geometric characterizations on Sasakian manifolds. We show that if a Sasakian metric g admits a non-trivial *-RB soliton, then it is -homothetically fixed null η-Einstein (transverse Calabi-Yau), and moreover, the soliton vector field is a non-strict infinitesimal contact transformation that leaves the structure tensor φ invariant and is a Jacobi field along trajectories of the Reeb vector field. Next, we explore contact RB almost solitons on almost contact α-cosymplectic 3-manifolds. We establish that such a space must have constant non-positive scalar curvature. It is also shown that a simply connected homogeneous α-cosymplectic 3-manifold admitting a contact RB almost soliton, under some hypothesis, is an uni-modular semidirect product Lie group G of type . Further, if µ ≠ 0, then G is the Lie group equipped with its flat left-invariant cosymplectic structure. And if µ = 0, then G is the abelian Lie group ℝ³ with its flat left-invariant cosymplectic structure.

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