In this paper, we define the intersection of similarity and metric equivalence relations. We investigate the resulting equivalence relation of operators(metro-similarity) acting on finite dimensional separable complex Hilbert spaces. We then give conditions under which two operators are metro-similar.
In this paper, we characterize Murray-von Neumann equivalent projections. We also investigate and compare the relationship between the Murray von Neumann relation and other equivalence relations on the set P (B (H)) of orthogonal projections in the von Neumann algebra B (H).
This paper deals with the study of -quasi-Einstein manifolds under certain curvature restrictions. We construct the non-trivial physical and geometrical examples of -quasi-Einstein manifolds, which validate the existence of such manifolds. The necessary and sufficient conditions for which the conformally and quasi-conformally flat -quasi-Einstein manifolds satisfy certain curvature restrictions are derived. We also prove that the generator of the manifold is a Killing vector field and the integral curves generated by the characteristic vector field are geodesics.
