On Lorentzian connections with parallel skew torsion

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Authors

ERNST Igor GALAEV Anton

Year of publication 2022
Type Article in Periodical
Magazine / Source Documenta Mathematica
MU Faculty or unit

Faculty of Science

Citation
Web https://ems.press/journals/dm/articles/13131898
Doi http://dx.doi.org/10.4171/DM/X31
Keywords holonomy; Lorentzianmanifold; naturally reductive homogeneous space; parallelskew-symmetric torsion; type II supergravity
Description 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.
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