Geometry of Ricci and $(\eta,\omega)$-Ricci solitons on the Sasaki–Kenmotsu manifold

UDC 514.7 We characterize the Sasaki–Kenmotsu manifold by using different kinds of solitons. Thus, we introduce a new type of solitons on the Sasaki–Kenmotsu manifold using a bicontact structure.  First, we observe the properties of the Ricci soliton on $(\eta,\omega)$-Sasaki–Kenmotsu manifold by using bicontact structure. Then we extended the $\eta$-Ricci soliton as an $(\eta,\omega)$-Ricci soliton and a conformal $\eta$-Ricci soliton as a conformal $(\eta,\omega)$-Ricci soliton by using the bicontact structure.