Geodesic
On Lorentzian connections with parallel skew torsion
Documenta mathematica, Tome 27 (2022), pp. 2333-2383.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The paper is devoted to metric connections with parallel skew-symmetric torsion in Lorentzian signature. This is motivated by recent progress in the Riemannian signature and by possible applications to supergravity theories. We provide a complete information about holonomy algebras, torsion and curvature of the considered connections up to the corresponding objects from the Riemannian signature. Various examples are constructed. It is shown how to construct all simply connected Lorentzian naturally reductive homogeneous spaces of arbitrary dimension from Riemannian naturally reductive homogeneous spaces. This leads to complete classification of Lorentzian naturally reductive homogeneous spaces in low dimensions.
Classification : 53B30, 53C29, 53C30
Keywords: Lorentzian manifold, parallel skew-symmetric torsion, holonomy, naturally reductive homogeneous space, type II supergravity 
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     title = {On {Lorentzian} connections with parallel skew torsion},
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Ernst, Igor; Galaev, Anton. On Lorentzian connections with parallel skew torsion. Documenta mathematica, Tome 27 (2022), pp. 2333-2383. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a8/