The C-connection and the 4-dimensional Einstein spaces

2024/09/26 by García-Parrado, Alfonso
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2409.17949

Abstract

We introduce a new family of operators in 4-dimensional pseudo-Riemannian manifolds with a non-vanishing Weyl scalar (non-degenerate spaces) that keep the conformal covariance of conformally covariant tensor concomitants. A particular case that arises naturally is the C-connection that is a Weyl connection that keeps conformal invariance. Using the C-connection we give a new characterization of non-degenerate spaces that are conformal to an Einstein space.

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