Flat Generalized Connections on Courant Algebroids

Gil R. Cavalcanti; Jaime Pedregal; Roberto Rubio

doi:10.1007/s00029-025-01083-0

Flat Generalized Connections on Courant Algebroids

Gil R. Cavalcanti, Jaime Pedregal^*, Roberto Rubio

^*Autor corresponent d’aquest treball

Utrecht University

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Resum

We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We find that the building blocks for such flat transitive Courant algebroids are compact simple Lie groups. Further, we give a description of left-invariant flat Levi-Civita generalized connections on such Lie groups, which, in particular, shows the existence of non-flat ones.

Idioma original	Anglès
Número d’article	84
Nombre de pàgines	34
Revista	Selecta Mathematica, New Series
Volum	31
Número	4
DOIs	https://doi.org/10.1007/s00029-025-01083-0
Estat de la publicació	Publicada - 9 de set. 2025

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10.1007/s00029-025-01083-0

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abstract = "We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We find that the building blocks for such flat transitive Courant algebroids are compact simple Lie groups. Further, we give a description of left-invariant flat Levi-Civita generalized connections on such Lie groups, which, in particular, shows the existence of non-flat ones.",

keywords = "Holonomy, Killing spinors, Ricci flow",

author = "Cavalcanti, \{Gil R.\} and Jaime Pedregal and Roberto Rubio",

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AU - Cavalcanti, Gil R.

AU - Pedregal, Jaime

AU - Rubio, Roberto

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PY - 2025/9/9

Y1 - 2025/9/9

N2 - We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We find that the building blocks for such flat transitive Courant algebroids are compact simple Lie groups. Further, we give a description of left-invariant flat Levi-Civita generalized connections on such Lie groups, which, in particular, shows the existence of non-flat ones.

AB - We consider a family of metric generalized connections on transitive Courant algebroids, which includes the canonical Levi-Civita connection, and study the flatness condition. We find that the building blocks for such flat transitive Courant algebroids are compact simple Lie groups. Further, we give a description of left-invariant flat Levi-Civita generalized connections on such Lie groups, which, in particular, shows the existence of non-flat ones.

KW - Holonomy

KW - Killing spinors

KW - Ricci flow

UR - https://www.scopus.com/pages/publications/105016138630

U2 - 10.1007/s00029-025-01083-0

DO - 10.1007/s00029-025-01083-0

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JO - Selecta Mathematica, New Series

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ER -

Flat Generalized Connections on Courant Algebroids

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