Bekaert, X.Morand, K.2019-11-142019-11-142018-07Journal of Mathematical Physics, 59(7), art. no. 0725030022-2488DOI: 10.1063/1.5030328http://repositorio.unab.cl/xmlui/handle/ria/10643Indexación: Scopus.We are grateful to Claude Barrabès for useful exchanges about null hypersurfaces. K.M. thanks the Institut des Hautes Études Scientifiques (IHÉS, Bures-sur-Yvette) for hospitality where part of this work was completed. The work of K.M. is supported by the Chilean Fondecyt Postdoc Project No. 3160325.Connections compatible with degenerate metric structures are known to possess peculiar features: on the one hand, the compatibility conditions involve restrictions on the torsion; on the other hand, torsionfree compatible connections are not unique, the arbitrariness being encoded in a tensor field whose type depends on the metric structure. Nonrelativistic structures typically fall under this scheme, the paradigmatic example being a contravariant degenerate metric whose kernel is spanned by a one-form. Torsionfree compatible (i.e., Galilean) connections are characterised by the gift of a two-form (the force field). Whenever the two-form is closed, the connection is said Newtonian. Such a nonrelativistic spacetime is known to admit an ambient description as the orbit space of a gravitational wave with parallel rays. The leaves of the null foliation are endowed with a nonrelativistic structure dual to the Newtonian one, dubbed Carrollian spacetime. We propose a generalisation of this unifying framework by introducing a new non-Lorentzian ambient metric structure of which we study the geometry. We characterise the space of (torsional) connections preserving such a metric structure which is shown to project to (respectively, embed) the most general class of (torsional) Galilean (respectively, Carrollian) connections. © 2018 Author(s).enArtículo