Ricci-like solitons on almost contact B-metric manifolds

Abstract

Ricci-like solitons with potential Reeb vector field are introduced and studied on almost contact B-metric manifolds. The cases of Sasaki-like manifolds and torse-forming potentials have been considered. In these cases, it is proved that the manifold admits a Ricci-like soliton if and only if the structure is Einstein-like. Explicit examples of Lie groups as 3- and 5-dimensional manifolds with the structures studied are provided.

arXiv comment13 pages

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Cited by in corpus (6)

• Ricci-like solitons with vertical potential on Sasaki-like almost contact B-metric manifolds
• Para-Ricci-like Solitons on Almost Paracontact Almost Paracomplex Riemannian Manifolds
• Almost Ricci-like solitons with torse-forming vertical potential of constant length on almost contact B-metric manifolds
• Yamabe solitons on conformal Sasaki-like almost contact B-metric manifolds
• Pairs of associated Yamabe almost solitons with vertical potential on almost contact complex Riemannian manifolds
• Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds