Related papers: Dimensional Reduction of Conformal Tensors and Ein…
We discuss the Kaluza-Klein reduction of spaces with (anti-)self-dual Weyl tensor and point out the emergence of the Einstein-Weyl equations for the reduction from four to three dimensions. As a byproduct we get a simple expression for the…
We study null alignment properties of Weyl tensors related via Kaluza$\unicode{x2013}$Klein reduction of vacuum spacetimes by one spatial Killing direction. Kaluza$\unicode{x2013}$Klein reduction is a method that relates spacetimes of…
Kaluza-Klein reduction of conformally flat spaces is considered for arbitrary dimensions. The corresponding equations are particularly elegant for the reduction from four to three dimensions. Assuming circular symmetry leads to explicit…
This paper presents conformal invariants for Riemannian manifolds of dimension greater than or equal to four whose vanishing is necessary for a Riemannian manifold to be conformally related to an Einstein space. One of the invariants is a…
Recently, the study of three-dimensional spaces is becoming of great interest. In these dimensions the Cotton tensor is prominent as the substitute for the Weyl tensor. It is conformally invariant and its vanishing is equivalent to…
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce…
In this paper we consider the Kaluza-Klein fields equations in presence of a generic 5D matter tensor which is governed by a conservation equation due to 5D Bianchi identities. Following a previous work, we provide a consistent approach to…
Given a super-integrable system in $n$ degrees of freedom, possessing an integral which is linear in momenta, we use the "Kaluza-Klein construction" in reverse to reduce to a lower dimensional super-integrable system. We give two examples…
The equations describing the Kaluza-Klein reduction of conformally flat spaces are investigated in arbitrary dimensions. Special classes of solution related to pseudo-Kahler and para-Kahler structures are constructed and classified…
Simple cosmological models based upon five-dimensional Kaluza-Klein relativity are re-examined and interesting properties are indicated. These models are special cases of those obtained by Davidson et al. and Mann and Vincent, specifically,…
On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives…
We consider Einstein-Maxwell-dilaton theory in four dimensions including the Kaluza-Klein theory and obtain the general asymptotic solutions in Bondi gauge. We find that there are three different types of news functions representing…
We study the Kaluza-Klein dimensional reduction of the Lovelock-Cartan theory in five-dimensional spacetime, with a compact dimension of $S^1$ topology. We find cosmological solutions of the Friedmann-Robertson-Walker class in the reduced…
During the last century, two independent theories using the concept of dimensional reduction have been developed independently. The first, known as F\"oppl-von K\`arm\`an theory, uses Riemannian geometry and continuum mechanics to study the…
We show that the Kaluza-Klein theory contains a fundamental problem: The four-dimensional metric tensor and the electromagnetic potential vector assumed in the Kaluza-Klein theory belong to four-dimensional vector spaces that are not…
We consider conformally invariant form of the actions in Einstein, Weyl, Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions($>2$) and investigate the relations among them. In Weyl space, the observational consistency…
A complete set of wave solutions is given for the weak field in a Kaluza-Klein theory with degenerate metric. In the five-dimensional version of this theory electromagnetism is described by two vector fields, and there is a reflection…
It is well known that the Kaluza-Klein monopole of Sorkin, Gross and Perry can be obtained from the Euclidean Taub-NUT solution with an extra compact fifth spatial dimension via Kaluza-Klein reduction. In this paper we consider…
We study the case in which the five dimensional theory is the transformed Weyl$-$Yang$-$Kaluza$-$Klein gravity. The dimensionally reduced equations of motion are derived by considering an alternative form of the main equation of the theory…
We examine the Kaluza-Klein (KK) dimensional reduction from higher-dimensional space-time and the properties of the resultant Bergmann-Wagoner general action of scalar-tensor theories. With the analysis of the perturbations, we also…