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

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.