The theory of a massive spin-2 state on the de Sitter space – with the mass squared equal to one sixth of the curvature – is special for two reasons: (i) it exhibits an enhanced local symmetry; (ii) it emerges as a part of the model that gives rise to the self-accelerated Universe. The known problems of this theory are: either it cannot be coupled to a non-conformal conserved stress-tensor beca...

We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The purpose of this paper is to study conformal deformation problems associated to conformal invariants on manifolds with boundary. From analysis point of view, the problem becomes a non-Dirichlet boundary value problems for ful...

The object of the present paper is to characterize pseudo Ricci symmetric twisted spacetimes. At first it shown that a spacetime GRW spacetime. Next, we obtain necessary and sufficient condition for be perfect fluid It also proved fluid, provided conformal curvature tensor divergence free. Moreover, investigate shear vorticity vector fields such type spacetimes pointed out its implications towa...

Theorem. Let gj = u;go be a sequence of conformal metrics satisfying the following conditions. (i) Vol(M, g) = eto for some positive constant eto. (ii) f R2(g) + Ip(gj)1 2 dJj ::; et2 for some positive constant et2 where R(g) is the scalar curvature of gj and p is the Ricci tensor of gj and dJj = u~ dVO. (iii) Al (g), the lowest eigenvalue of the Laplacian of the metric gj' has a positive lower...

Some years ago Koutras presented a method of constructing a conformal Killing tensor from a pair of orthogonal conformal Killing vectors. When the vector associated with the conformal Killing tensor is a gradient, a Killing tensor (in general irreducible) can then be constructed. In this paper it is shown that the severe restriction of orthogonality is unnecessary and thus it is possible that m...

The goal of this paper is to express the Bach tensor of a four dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang–Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach te...

We review the theory of orthogonal separation of variables of the Hamilton– Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal Killing tensor, hereafter called a concircular tensor. First, we show how to extend original results given by Benenti to intrinsically characterize all (orthog...

In this proceeding, we review modified theories of gravity with a curvature-matter coupling between an arbitrary function the scalar curvature and Lagrangian density matter. This explicit nonminimal induces non-vanishing covariant derivative energy-momentum tensor, that implies non-geodesic motion consequently leads to appearance extra force. Here, explore physical cosmological implications non...

We present some results in [9], a continuation of our earlier works [7] and [8]. One result is the existence and compactness of solutions to a fully nonlinear version of the Yamabe problem on locally conformally flat Riemannian manifolds, and the other is a Harnack type inequality for general conformally invariant fully nonlinear second order elliptic equations. Let (M, g) be an n−dimensional, ...

The diagonalization of the metrical and canonical Hamilton operators of a scalar field with an arbitrary coupling, with a curvature in N-dimensional homogeneous isotropic space is considered in this paper. The energy spectrum of the corresponding quasiparticles is obtained and then the modified energy-momentum tensor is constructed; the latter coincides with the metrical energy-momentum tensor ...