Executive Summary : | Contact geometry is increasingly important in mechanics for understanding physical phenomena. Recent articles have explored the self-similar solutions of the Ricci flow equation, i.e., Ricci solitons, for contact metric geometry. Some studies find conditions when a contact manifold with a Ricci-type soliton structure carries a canonical metric. This paper proposes weakening one of these conditions and investigating the geometry of weak structures. The weak K-contact structure is useful for studying unit Killing vector fields on Riemannian manifolds, and some results for K-contact manifolds can be extended to weak K-contact manifolds. The study aims to investigate weak analogues of weak almost contact structures, such as weak K-contact and weak Sasakian, and the results of Einstein-type manifolds on these structures. |