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A more accessible summary of odd generalized Einstein metrics

Published on:

1 November 2023

Primary Category:

Differential Geometry

Paper Authors:

Vicente Cortés,

Liana David

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Key Details

Classifies odd generalized Einstein metrics on 3-dimensional Lie groups

Uses canonical forms of two key operators relating Lie bracket, metric and Courant algebroid

Studies unimodular groups first, leading to examples on SO(3), SO(2,1) etc

Then treats non-unimodular groups, completing the classification

AI generated summary

A more accessible summary of odd generalized Einstein metrics

This paper classifies odd generalized Einstein metrics on 3-dimensional Lie groups. These are a type of geometric structure defined on Courant algebroids, which are mathematical objects generalizing tangent bundles. The classification relies on the canonical forms of two key operators: the first relates the Lie bracket to the metric, and the second is associated to the Courant algebroid. After introducing basic concepts, the 3-dimensional case is studied. First unimodular Lie groups are considered, leading to examples on SO(3), SO(2,1), the Heisenberg group and others. Then non-unimodular Lie groups are treated, completing the classification.

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