CL-Transformation on 3-Dimensional Quasi Sasakian Manifolds and Their Ricci Soliton

This paper explores the geometry of 3-dimensional quasi Sasakian manifolds under CL-transformations. We construct both infinitesimal and CL-transformation and demonstrate that the former does not necessarily yield projective killing vector fields. A novel invariant tensor, termed the CL-curvature tensor, is introduced and shown to remain invariant under CL-transformations. Utilizing this tensor, we characterize CL-flat, CL-symmetric, CL-φ symmetric and CL-φ recurrent structures on such manifolds by mean of differential equations. Furthermore, we investigate conditions under which a Ricci soliton exists on a CL-transformed quasi Sasakian manifold, revealing that under flat curvature, the structure becomes Einstein. These findings contribute to the understanding of curvature dynamics and soliton theory within the context of contact metric geometry.