Three-Diffeomorphism Conformal Space over Lorentzian Manifold

TL;DR

This paper introduces a novel conformal space constructed from three diffeomorphisms over Lorentzian manifolds, utilizing a Borel measure and a piecewise-Riemannian scalar product, with implications for diffeoinvariant measures.

Contribution

It defines a new conformal space based on three diffeomorphisms over Lorentzian manifolds, incorporating a diffeoinvariant measure and a scalar product, advancing geometric analysis methods.

Findings

Construction of a conformal space from three diffeomorphisms.

Introduction of a diffeoinvariant measure on Lorentzian manifolds.

Examples illustrating the properties of the conformal space.

Abstract

Through making use of a Borel measure and a piecewise-Riemannian inner scalar product, it is shown that over a Lorentzian manifold every three diffeomorphisms generate a conformal space, whose elements are smooth vector-valued functions equipped with compact supports. Few examples, in particular a diffeoinvariant measure, are provided with respect to an arbitrary smooth function introduced as into consideration as a multiplier to a local scale factor.