The asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) metric defines invariants of the AHE metric and of a metric in the induced conformal class at infinity. These have been of recent interest, motivated in part by the AdS/CFT correspondence in physics. In this paper we derive some new properties of these invariants. Let (X, g+) be AHE with smooth conformal infin...

‎We study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry property‎. ‎We then consider Einstein-like metrics‎, ‎Ricci solitons and homogeneity over these spaces‎‎.

It is given a complete study of locally conformally flat metrics satisfying some weakly-Einstein conditions. shown that they are either product Mn(c)×Mn(−c) or warped R×fRn−1 for specific warping function. Moreover, conditions on fixed points the RG2 flow pointed out.

In this paper, we study gradient Einstein-type structure immersed into a Riemannian warped product manifold. We obtain some triviality results for the potential function and smooth map u . investigate conditions to be totally umbilical, or geodesic I × f M n Furthermore, rotational hypersurface R has structure.