This is the first of two papers where we address and partially confirm a conjecture of Deser and Schwimmer, originally postulated in high energy physics, [10]. The objects of study are scalar Riemannian quantities constructed out of the curvature and its covariant derivatives, whose integrals over compact manifolds are invariant under conformal changes of the underlying metric. Our main conclus...

We investigate the possibility that the conformal and conformal thin sandwich (CTS) methods can be used to parameterize the set of solutions of the vacuum Einstein constraint equations. To this end we develop a model problem obtained by taking the quotient of certain symmetric data on conformally žat tori. Specializing the model problem to a three-parameter family of conformal data we observe a...

We examine theories of gravity which include finitely many coupled scalar fields with arbitrary couplings to the curvature (wavemaps). We show that the most general scalar-tensor σ-model action is conformally equivalent to general relativity with a minimally coupled wavemap with a particular target metric. Inflation on the source manifold is then shown to occur in a novel way due to the combine...

This paper aims to study some semi-symmetric and curvature tensor conditions on α-Kenmotsu pseudo-metric manifolds. Some of semi-symmetric, locally symmetric, the Ricci are considered such Also, relationships between M-projective conformal tensor, concircularly conharmonic investigated. Finally, an example structure is given.

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...

Abstract In this article, we investigate perfect fluid spacetimes equipped with concircular vector field. At first, in a spacetime admitting field, prove that the velocity field annihilates conformal curvature tensor. addition, dimension 4, show is generalized Robertson–Walker Einstein fibre. It proved if furnished admits second order symmetric parallel tensor P , then either equation of state ...