A Diagram for Bianchi A-Types

TL;DR

This paper introduces a diagrammatic representation for Bianchi A-type spaces, illustrating their relationships and transformations, with a focus on Ricci coefficients and tensors linked via Cremona transformations.

Contribution

It provides a new diagrammatic tool to visualize the relations among Bianchi A-type spaces and their Ricci properties, enhancing understanding of their geometric structure.

Findings

Diagram effectively illustrates Bianchi A-type relations

Cremona transformation links Ricci coefficients and tensors

Clarifies geometric transformations among Bianchi spaces

Abstract

A diagram for Bianchi spaces with vanishing vector of structure constants (type A in the Ellis-MacCallum classification) illustrates the relations among their different types under similarity transformations. The Ricci coefficients and the Ricci tensor are related by a Cremona transformation.