صندلی اداری

RICCI-LIKE SOLITONS ON ALMOST CONTACT B-METRIC MANIFOLDS: A REVIEW

Mancho Manev

Abstract


An overview of five papers by the author from the last two yearson the topic has been made. Ricci-like solitons are introduced and studied on almostcontact B-metric manifolds (also known as almost contact complex Riemannian manifolds)in the cases when the soliton’s potential is the Reeb vector field, vertical orarbitrary vector field. The cases of Sasaki-like manifolds and torse-forming potentialshave been considered. In these cases, necessary and sufficient conditions are provedthese manifolds are (almost) Einstein-like. Explicit examples of Lie groups as 3- and5-dimensional manifolds with the structures studied are provided. Some generalizationsof these solitons are considered: almost Ricci-like solitons and gradient almost Ricci-likesolitons.

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