Narrow Results

In this paper we study 3-dimensional contact metric manifolds satisfying certain conditions on the tensor fields *-Ricci tensorS*, h(= ½L_ξφ), τ(= L_ξg = 2hφ) and the Ricci operator Q. First, we prove that a 3-dimensional non-Sasakian contact metric manifold satisfies.

In [30], Tachibana introduced the notion of ^*-Ricci tensor on almost Hermitian manifolds. Motivated by the previous work, Hamada [18] defined ^*-Ricci tensors of real hypersurfaces in non-flat complex space forms. Using ^*-Ricci tensors, in [20], the authors introduced the notion of ^*-Ricci solitons of real hypersurfaces in non-flat complex space forms. This short note aims to present the progress in the study of ^*-Ricci soliton.

We investigate geometric properties of 3-dimensional real hypersurfaces with Aξ = 0 in a complex 2-dimensional nonflat complex space form from the view-points of their shape operators, Ricci tensors and *-Ricci tensors.