Published on:

1 November 2023

Primary Category:

Differential Geometry

Paper Authors:

Vicente Cortés,

Liana David

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Classifies odd generalized Einstein metrics on 3-dimensional Lie groups

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

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

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Then treats non-unimodular groups, completing the classification

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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