nLab stable form

Idea

In the context of differential geometry and special holonomy, a stable form (Hitchin, def. 1.1) is an element $\phi$ in some exterior power $\wedge^p V$ of some vector space $V$,such that the orbit of this element under the action of the general linear group $GL(V)$ is open.

The stabilizer groups of such stable forms correspond to flavors of special holonomy.

Related concepts

• definite form

References

• Nigel Hitchin, Special holonomy and beyond, Clay Mathematics Proceedings (pdf)