Abstract Motivated by constant-G theory, we introduce a one-parameter family of scalar–tensor theories as an extension theory in which the conformal symmetry is cosmological attractor. Since model has coupling function negative curvature, expect spontaneous scalarization to occur and that parameter can be constrained pulsar timing measurements. Modeling neutron stars with realistic equations st...

Scale-invariant actions in arbitrary dimensions are investigated in curved space to clarify the relation between scale-, Weyland conformal invariance on the classical level. The global Weyl-group is gauged. Then the class of actions is determined for which Weyl-gauging may be replaced by a suitable coupling to the curvature (Ricci gauging). It is shown that this class is exactly the class of ac...

The purpose of this note is to provide yet another example of the link between certain conformal geometries and ordinary differential equations, along the lines of the examples discussed by Nurowski [3]. In this particular case, I consider the equivalence problem for 3-plane fields D ⊂ TM on a 6-manifold M satisfying the nondegeneracy condition that D + [D, D] = TM . I give a solution of the eq...

The gauged SL(2,R)/U(1) Wess-Zumino-Novikov-Witten (WZNW) model is classically an integrable conformal field theory. We have found a Lax pair representation for the non-linear equations of motion, and a Bäcklund transformation. A second-order differential equation of the Gelfand-Dikii type defines the Poisson bracket structure of the theory, and its fundamental solutions describe the general so...

An analysis of one and two point functions of the energy momentum tensor on homogeneous spaces of constant curvature is undertaken. The possibility of proving a c-theorem in this framework is discussed, in particular in relation to the coefficients c, a, which appear in the energy momentum tensor trace on general curved backgrounds in four dimensions. Ward identities relating the correlation fu...

in this paper, the matsumoto metric with special ricci tensor has been investigated. it is proved that, if  is ofpositive (negative) sectional curvature and f is of  -parallel ricci curvature with constant killing 1-form ,then (m,f) is a riemannian einstein space. in fact, we generalize the riemannian result established by akbar-zadeh.

Abstract We study two natural problems concerning the scalar and Ricci curvatures of Bismut connection. Firstly, we an analog Yamabe problem for Hermitian manifolds related to curvature, proving that, fixed a conformal structure on compact complex manifold, there exists metric with constant curvature in that class when expected is non-negative. A similar result given general case Gauduchon conn...

In this note, we compare two different definitions for the cosmological perturbation $\zeta$ which is conserved on large scales, and study their non-conservation small scales. We derive an equation time evolution of curvature a uniform density slice through calculation solely in longitudinal (conformal-Newtonian) gauge. The result concise compatible with that obtained via local conservation ene...

The diagonalization of the metrical Hamiltonian of a scalar field with an arbitrary coupling with a curvature in N -dimensional homogeneous isotropic space is performed. The energy spectrum of the corresponding quasiparticles is obtained. The energies of the quasiparticles corresponding to the diagonal form of the canonical Hamiltonian are calculated. The modified energy-momentum tensor with th...

In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize standard 4-sphere. We obtain a gap theorem, for Yamabe positive scalar curvature $L^2$ norm Weyl tensor metric suitably small, establish monotonic decay $L^p$ certain $p>2$ reduced along normalized flow, converging exponentially to