相关论文: On the intrinsic torsion of spacetime structures

We study $D$-dimensional $p$-brane Galilean geometries via the intrinsic torsion of their adapted connections. These non-Lorentzian geometries are examples of $G$-structures whose characteristic tensors consist of two degenerate ``metrics''…

It is well-known that unlike space-like and time-like hypersurfaces, null hypersurfaces in Lorentzian manifolds do not naturally inherit an affine connection from the spacetime in which they are embedded. On the other hand, recent…

Motivated by the thermodynamics of black hole solutions conformal to stationary solutions, we study the geometric invariant theory of null hypersurfaces. It is well-known that a null hypersurface in a Lorentzian manifold can be treated as a…

We develop a classification of general Carrollian structures, permitting affine connections with both torsion and non-metricity. We compare with a recent classification of general Galilean structures in order to present a unified…

We study the geometry of foliated non-Lorentzian spacetimes in terms of the Godbillon-Vey class of the foliation. We relate the intrinsic torsion of a foliated Aristotelian manifold to its Godbillon-Vey class, and interpret it as a measure…

This article introduces the problem of finding intrinsic torsion varieties associated to G-structures on a fixed parallelizable Riemannian manifold. As an illustration, the intrinsic torsion varieties of orthogonal almost product structures…

We study the concept of Carrollian spacetime starting from its underlying fiber-bundle structure. The latter admits an Ehresmann connection, which enables a natural separation of time and space, preserved by the subset of Carrollian…

We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…

The following three geometrical structures on a manifold are studied in detail: (1) Leibnizian: a non-vanishing 1-form $\Omega$ plus a Riemannian metric $\h$ on its annhilator vector bundle. In particular, the possible dimensions of the…

The aim of this series of papers is to generalise the ambient approach of Duval et al. regarding the embedding of Galilean and Carrollian geometries inside gravitational waves with parallel rays. In this first part, we propose a…

We discuss the generalized Newton-Cartan geometries that can serve as gravitational background fields for particles and strings. In order to enable us to define affine connections that are invariant under all the symmetries of the structure…

Carrollian physics provides the natural framework for describing null hypersurfaces. This review explores the geometry of Carrollian manifolds -- spaces endowed with a degenerate metric. We begin with an algebraic overview of the Carroll…

I review some of my recent work on non-lorentzian geometry. I review the classification of kinematical Lie algebras and their associated Klein geometries. I then describe the Cartan geometries modelled on them and their characterisation in…

The existence of topological invariants analogous to Chern/Pontryagin classes for a standard $SO(D)$ or $SU(N)$ connection, but constructed out of the torsion tensor, is discussed. These invariants exhibit many of the features of the…

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…

We give a full classification of general affine connections on Galilei manifolds in terms of independently specifiable tensor fields. This generalises the well-known case of (torsional) Galilei connections, i.e. connections compatible with…

Curvature and torsion are the two tensors characterizing a general Riemannian spacetime. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the…

Within the generalized Newton-Cartan theory, Galilean Twisted spacetimes are introduced as dual models of the well-known relativistic twisted spacetimes. As a natural generalization, torqued vector fields in Galilean spacetimes are defined,…

We study the types of non-integrable $\mathrm{G}$-structures on Riemannian manifolds. In particular, geometric types admitting a connection with totally skew-symmetric torsion are characterized. 8-dimensional manifolds equipped with a…

Using the recently advanced Galilean gauge theory (GGT) we give a comprehensive construction of torsional Newton Cartan geometry. The coupling of a Galilean symmetric model with background NC geometry following GGT is illustrated by a free…