nLab
pseudo-orthogonal structure

Contents

Idea

The concept of pseudo-orthogonal structure is the analog of that of orthogonal structure as one generalized from Euclidean signature to Lorentzian signature.

Given a smooth manifold XX of dimension nn, then a pseudo-orthogonal structure of XX is a reduction of the structure group of its frame bundle along the inclusion O(n1,1)GL(n)O(n-1,1) \hookrightarrow GL(n) of the Lorentz group into the general linear group.

In physics, specifically in the first-order formulation of gravity, such a G-structure is often called a vielbein field.

A pseudo-orthogonal structure induces a pseudo-Riemannian metric on XX.

Created on July 22, 2017 at 10:08:12. See the history of this page for a list of all contributions to it.