In this paper we study a Riemanian metric on the tangent bundle T (M) of a Riemannian manifoldM which generalizes Sasakian metric and Cheeger–Gromoll metric along a compatible almost complex structure which together with the metric confers to T (M) a structure of locally conformal almost Kählerian manifold. This is the natural generalization of the well known almost Kählerian structure on T (M)...

In this paper, we give a new lower bound for the eigenvalues of the Dirac operator on a compact spin manifold. This estimate is motivated by the fact that in its limiting case a skew-symmetric tensor (see Equation (1.6)) appears that can be identified geometrically with the O’Neill tensor of a Riemannian flow, carrying a transversal parallel spinor. The Heisenberg group which is a fibration ove...

Recently, K. Matsumoto and I. Mihai established a sharp inequality for warped products isometrically immersed in Sasakian space forms. As applications, they obtained obstructions to minimal isometric immersions of warped products into Sasakian space forms. P. Alegre, D.E. Blair and A. Carriazo have introduced the notion of generalized Sasakian space form. In the present paper, we obtain a sharp...

In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2-connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit regular positive Sasakian structures.

The geometry of manifolds endowed with geometrical structures has been intensively studied, and several important results have been published. In this paper, we deal with manifolds having a Lorentzian concircular structure LCS n-manifold 1–3 see Section 2 for detail . The study of the Lorentzian almost paracontact manifold was initiated by Matsumoto in 4 . Later on, several authors studied the ...