# Torsional Newton–Cartan geometry and the Schrödinger algebra

@article{Bergshoeff2014TorsionalNG,
title={Torsional Newton–Cartan geometry and the Schr{\"o}dinger algebra},
author={Eric Bergshoeff and Jelle Hartong and Jan Rosseel},
journal={Classical and Quantum Gravity},
year={2014},
volume={32},
pages={135017}
}
• Published 19 September 2014
• Physics
• Classical and Quantum Gravity
We show that by gauging the Schrodinger algebra with critical exponent z and imposing suitable curvature constraints, that make diffeomorphisms equivalent to time and space translations, one obtains a geometric structure known as (twistless) torsional Newton-Cartan geometry (TTNC). This is a version of torsional Newton-Cartan geometry (TNC) in which the timelike vielbein t mu must be hypersurface orthogonal. For z = 2 this version of TTNC geometry is very closely related to the one appearing in… Expand

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