# Category:Differential manifolds with reduced structure group

From Diffgeom

The smaller the structure group, the stronger the structure on the differential manifold. In other words, a differential manifold with a given structure group automatically has any bigger group containing that, as structure group. The important subgroups of the general linear group occurring here are:

- which corresponds to almost Hermitian manifold
- which contains and corresponds to almost complex manifold. Thus almost Hermitian manifold is a stronger structure than almost complex manifold.
- which contains and corresponds to almost symplectic manifold. Thus almost Hermitian manifold is a stronger structure than almost symplectic manifold.
- which corresponds to Riemannian manifold. When , this contains . Thus, almost Hermitian manifold is a stronger structure than Riemannian manifold
- which contains when , and corresponds to oriented manifold. Thus oriented manifold is a stronger structure than almost symplectic manifold.

Lorentzian and pseudo-Riemannian manifolds correspond to pseudo-orthogonal groups and .

## Pages in category "Differential manifolds with reduced structure group"

The following 7 pages are in this category, out of 7 total.