On Lorentzian connections with parallel skew torsion
Igor Ernst
Masaryk University, Department of Mathematics and Statistics, Faculty of Science, Kotlářská 2, 611 37 Brno, Czech RepublicAnton Galaev
University of Hradec Králové, Faculty of Science, Rokitanského 62, 500 03 Hradec Králové, Czech Republic
Abstract
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.
Cite this article
Igor Ernst, Anton Galaev, On Lorentzian connections with parallel skew torsion. Doc. Math. 27 (2022), pp. 2333–2383
DOI 10.4171/DM/X31