A Euclidean Bianchi Model Based On $S^3/D_8^*$

TL;DR

This paper constructs a Euclidean Bianchi type IX cosmological model by slicing the four-sphere along specific homogeneous 3-manifolds, exploring its geometric properties within Einstein's equations with a cosmological constant.

Contribution

It introduces a novel Euclidean Bianchi model based on the four-sphere and analyzes its geometric characteristics, extending the understanding of homogeneous cosmologies.

Findings

Defines a Euclidean Bianchi type IX model from $S^3/D_8^*$ slices

Analyzes the geometric properties of the model

Provides insights into Einstein's equations with a cosmological constant

Abstract

We explain how the round four-sphere can be sliced along homogeneous 3~-~manifolds of topology $S^3/D_8^*$. This defines a Euclidean Bianchi type IX model for Einstein's equations with cosmological constant. The geometric properties of this model are investigated.