We show that every measurable invariant conformal structure for a Hölder continuous linear cocycle over a subshift of finite type coincides almost everywhere with a continuous invariant conformal structure. We use this result to establish Hölder continuity of a measurable conjugacy between Hölder continuous cocycles where one of the cocycles is assumed to be uniformly quasiconformal. As a speci...

This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface into Euclidean 3-space. As applications, we construct a 2-parameter family of non-minimal conformal biharmonic immersions of cylinder into R and ...

It is shown how one can do symplectic reduction for locally conformal symplectic manifolds, especially with an action of a Lie group. This generalizes well known procedures for symplectic manifolds to the slightly larger class of locally conformal symplectic manifolds. The whole setting is very conformally invariant.

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 The conformal anomaly for 4D gravity-matter theories, which are non-minimally coupled with the dilaton, is systematically studied. Special care is taken for: rescaling of fields, treatment of total derivatives, hermiticity of the system operator and choice of measure. Scalar, spinor and vector fields are taken as the matter quantum fields and their explicit conformal anomalies in the g...