Almost $\eta$-conformal Ricci solitons in $(LCS)_{3}$-manifolds

Abstract

The aim of the present paper is to study the properties of three dimensional Lorentzian concircular structure manifolds ($(LCS)_{3}$-manifolds) endowed with almost $\eta$-conformal Ricci solitons. Also, we discuss the $\eta$-conformal gradient shrinking Ricci solitons on $(LCS)_{3}$-manifolds. Finally, the examples of almost $\eta$-conformal Ricci soliton on an $(LCS)_{3}$-manifold are provided in the region where $(LCS)_{3}$-manifold is expanding.