A semisymmetric metric connection on almost contact B-metric manifolds

Abstract

The object of the present paper is to study a semisymmetric metric connection on an almost contact B-metric manifold. We deduce a relation between the Levi-Civita connection and the semisymmetric metric connection on the considered manifold. We determined the class of the torsion tensor corresponding to the semisymmetric connection. We study Ricci-like solitons on almost contact B-metric manifolds with the semisymmetric connection. Finally, we give some examples to considered manifolds with the semisymmetric connection.