arXiv subjects

M. Limoncu

Publications and source records attributed to M. Limoncu.

3 recordsLinked to original sources

arXiv2007

Linear Connections on Light-like Manifolds

It is well-known that a torsion-free linear connection on a light-like manifold $(M,g)$ compatible with the degenerate metric $g$ exists if and only if $Rad(TM)$ is a Killing distribution. In case of existence, there is an infinitude of connections with none distinguished. We propose a method to single out connections with the help of a special set of 1-forms by the condition that the 1-forms become parallel with respect to this connection. Such sets of 1-forms could be regarded as an additional structure imposed upon the light-like manifold. We consider also connections with torsion and with non-metricity on light-like manifolds.

math.DG↗

arXiv2006

Degenerate Spin Structures and the Levy-Leblond Equation

Newton-Cartan manifolds and the Galilei group are defined by the use of co-rank one degenerate metric tensor. Newton-Cartan connection is lifted to the degenerate spinor bundle over a Newton-Cartan 4-manifold by the aid of degenerate spin group. Levy-Leblond equation is constructed with the lifted connection.

math-ph↗

arXiv2004

Newton-Cartan connections with torsion

We re-formulate the notion of a Newton-Cartan manifold and clarify the compatibility conditions of a connection with torsion with the Newton-Cartan structure.

gr-qc↗