The object of this paper is to study (k, μ)-paracontact metric manifolds with qusi-conformal curvature tensor. It has been shown that, h-quasi conformally semi-symmetric and φ-quasi-conformally semi-symmetric (k, μ)-paracontact metric manifold with k 6= −1 cannot be an η-Einstein manifold.

In this note, we prove an existence result for the Einstein conformal constraint equations metrics with vanishing Yamabe invariant assuming that mean curvature satisfies explicit near-CMC condition and TT-tensor is small in $$L^2$$ .

Abstract We analyze the stress-energy tensor, and the resulting energy conditions, for a scalar field with general curvature coupling, outside a perfectly reflecting sphere with Dirichlet boundary conditions. For conformal coupling we find that the null energy condition is always obeyed, and therefore the averaged null energy condition (ANEC) is also obeyed. Since the ANEC is independent of cur...

Once the action for Einstein’s equations is rewritten as a functional of an SO(3, C) connection and a conformal factor of the metric, it admits a family of “neighbours” having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in ...

At high energy scale the only quantum effect of any asymptotic free and asymptoti-cally conformal invariant GUT is the trace anomaly of the energy-momentum tensor. Anomaly generates the new degree of freedom, that is propagating conformal factor. At lower energies conformal factor starts to interact with scalar field because of the violation of conformal invari-ance. We estimate the effect of s...

Let (M, g) be an asymptotically locally hyperbolic (ALH) manifold which is the interior of a conformally compact manifold and (∂M, [γ]) its conformal infinity. Suppose that the Ricci tensor of (M, g) dominates that of the hyperbolic space and that its scalar curvature satisfies a certain decay condition at infinity. If the Yamabe invariant of (∂M, [γ]) is non-negative, we prove that there exist...