Honam Mathematical J. 42 (2020), No. 3, pp. 521–536 https://doi.org/10.5831/HMJ.2020.42.3.521 ALMOST QUASI-YAMABE SOLITONS ON LORENTZIAN CONCIRCULAR STRUCTURE MANIFOLDS-[(LCS ) n ] Jae-Bok Jun ∗ and Mohd. Danish Siddiqi Abstract. The object of the present paper is to study of Almost Quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons on an Lorentzian concircular structure manifolds briefly say (LCS)n -manifolds under infinitesimal CL-transformations and obtained sufficient conditions for such solitons to be expanding, steady and shrinking. Also we obtained a necessary and sufficient condition of an almost quasi-Yamabe soliton with respect to the CL-connection to be an almost quasi-Yamabe soliton on (LCS)n-manifolds with respect to Levi-Civita connection. Finally, we construct an example of steady almost quasi-Yamabe soliton on 3-dimensional (LCS)n- manifolds. 1. Introduction The Yamabe problem in differential geometry concerns the existence of Riemannian metrics with constant scalar curvature, and takes its name from the mathematician Hidehiko Yamabe in 1960. In differential geometry, the Yamabe flow is an intrinsic geometric flow in a process which deforms the metric of a Riemannian manifold. The fixed points of the Yamabe flow are metrics of constant scalar curvature in the given conformal class which is first introduced by R. S. Hamilton [7] by the following equation (1) ∂ ∂t g(t)= −r(t)g(t), Received November 28, 2019. Revised May 20, 2020. Accepted June 9, 2020. 2010 Mathematics Subject Classification. 53C15, 53C20, 53C25, 53C44. Key words and phrases. Almost quasi-Yamabe soliton, gradient almost quasi-Yamabe soliton, (LCS)n-manifolds, infinitesimal CL-transformations, scalar curvature. *Corresponding author