A characterization of conformally flat spaces

Kaluza-klein Reduction of Conformally Flat Spaces

A “conformal tensor” is constructed from the metric tensor gMN (or Vielbein e A M ) and is invariant against Weyl rescaling gMN → egMN (or eM → eeM ). Moreover, it vanishes if and only if the space is conformally flat, gMN = e ηMN (or e A M = eδ M ). In dimension four or greater the conformal tensor is the Weyl tensor. In three dimensions the Weyl tensor vanishes identically, while the Cotton t...

A Characterization of Certain Conformally Euclidean Spaces of Class One

1. In this paper we will examine the metrics of conformally Euclidean spaces Cn (n^A) having the following two properties: (1) They are locally and isometrically imbeddable in Euclidean space of one higher dimension (£n+i), i.e. they are of class one. (2) With respect to a conformai coordinate system, the matrix of the second fundamental tensor [èy] has diagonal form. The condition for class on...

Compactification of a Class of Conformally Flat 4-manifold

Conformally Flat Lorentzian Three-spaces with Various Properties of Symmetry and Homogeneity

We study conformally flat Lorentzian three-manifolds which are either semi-symmetric or pseudo-symmetric. Their complete classification is obtained under hypotheses of local homogeneity and curvature homogeneity. Moreover, examples which are not curvature homogeneous are described.

Twistors in Conformally Flat Einstein Four-manifolds

Abstract. This paper studies the two-component spinor form of massive spin2 potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a nonvanishing cosmological constant makes it necessary to introduce a supercovariant derivative operator. The analysis of supergauge transformations of primary and secondary potentials for spin 3 2 shows that the gauge fre...