The generating function of correlators of dual operators on the boundary of (A)dS4 space corresponding to the conformally coupled φ 4-model is obtained up to first order in the coupling constant by using the conformal map between massless scalar fields in (Euclidean) Minkowski space and conformally coupled scalars on (Euclidean anti) de Sitter space. Some exact classical solutions of the nonlin...

The energy-momentum tensor for a massless conformally coupled scalar field in the region between two parallel plates moving by uniform proper accelerations in k = −1 Robertson–Walker spacetime is investigated. We assume that the scalar field satisfies the Dirichlet boundary condition on the plates. k = −1 Robertson– Walker space is conformally related to the Rindler space, as a result we can ob...

The energy-momentum tensor for a massless conformally coupled scalar field in the region between two curved boundaries in k = −1 static Robertson–Walker spacetime is investigated. We assume that the scalar field satisfies the Dirichlet boundary condition on the boundaries. k = −1 Robertson–Walker space is conformally related to the Rindler space, as a result we can obtain vacuum expectation val...

Alice Chang’s Question: A very general question is to ask “What is the geometric content of Q-curvature?” For example, we know that one can associate the scalar curvature with the conformally invariant constant called the “Yamabe constant”. When this constant is positive, it describes the best constant (in a conformally invariant sense) of the Sobolev embedding of W 1,2 into L space; this in it...

The aim of the present paper is to study properties of Quasi conformally flat LP-Sasakian manifolds with a coefficient α. In this paper, we prove that a Quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α is an η−Einstein and in a quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α if the scalar curvature tensor is constant then M ...

We inv estigate the applicability of an adaptive neural network to problems with time-dependent input by demonstrating that a deterministic parser for natural language inputs of significant syntactic complexity can be developed using recurrent connectionist architectures. The traditional stacking mechanism, known to be necessary for proper treatment of context-free languages in symbolic systems...

É. Cartan proved that conformally flat hypersurfaces in Sn+1 for n > 3 have at most two distinct principal curvatures and locally envelop a one-parameter family of (n − 1)-spheres. We prove that the Gauss-Codazzi equation for conformally flat hypersurfaces in S4 is a soliton equation, and use a dressing action from soliton theory to construct geometric Ribaucour transforms of these hypersurface...