We classify conformally flat Riemannian 3−manifolds which possesses a free isometric S−action.

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...

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...

Here we will consider examples of conformally flat manifolds that are conformally equivalent to open subsets of the sphere S. For such manifolds we shall introduce a Cauchy kernel and Cauchy integral formula for sections taking values in a spinor bundle and annihilated by a Dirac operator, or generalized Cauchy-Riemann operator. Basic properties of this kernel are examined, in particular we exa...

We present a novel approach to creating flat maps of the brain. Our approach attempts to preserve the conformal structure between the original cortical surface in 3-space and the flattened surface. We demonstrate this with data from the human cerebellum. Our maps exhibit quasiconformal behavior and offer several advantages over existing approaches.

We prove that for each closed smooth spin 4-manifold M there exists a closed smooth 4-manifold N such that M#N admits a conformally flat Riemannian metric.

Conformally flat spherically symmetric cosmological models representing a charged perfect fluid as well as a bulk viscous fluid distribution have been obtained. The cosmological constant Λ is found positive and is a decreasing function of time which is consistent with the recent supernovae observations. The physical and geometrical properties of the models are discussed.