Almost Yamabe Solitons And K-Contact Geometry

In this paper,the properties of soliton fields of almost Yamabe solitons,almostδ-Yamabe solitons and almost η-Yamabe solitons are studied on K-contact metric manifolds.By using the methods of covariant differential operator,Lie derivative operator and exterior differential operator,and introduces respectively the characteristics of a K-contact metric g represents an almost Yamabe soliton with the soliton field is contact,almost δ-Yamabe solitons on contact metric manifolds satisfy certain contact structures and properties of almost η-Yamabe solitons in K-contact geometry.The main results obtained in this paper include:1.It is proved that the soliton fields of almost Yamabe solitons in K-contact metric manifolds are Killing vector fields.2.The section studies that a contact metric of contact metric manifold is an almost δ-Yamabe soliton when certain conditions are satisfied and its soliton field is a Killing vector field.3.It is proved that the nontrivial almost η-Yamabe solitons on contact metric manifolds are K-contact metrics when certain conditions are satisfied,and then proved that the soliton fields of almost η-Yamabe solitons on K-contact metric manifolds are Killing vector fields.