Manifolds admitting stable forms. (English) Zbl 1212.53051

Lê, Hông-Vân; Panák, Martin; Vanžura, Jiří

Commentat. Math. Univ. Carol. 49, No. 1, 101-117 (2008).

A \(k\)-form \(\gamma \) on a (real or complex) vector space \(V^n\) is stable if its orbit \(GL(n)(\gamma)\) is open in \({\Lambda }^k(V^n)^*\); stable forms are multi-symplectic. A method presented in the paper allows to classify stable forms on real \(n\)-dimensional space and find their automorphism groups. Some necessary conditions, and also sufficient conditions for a manifold to admit a stable form are given, some interesting examples and consequences are presented.

Reviewer: Alena Vanžurová (Olomouc)

MSC:

53C15

General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords:

stable forms; automorphism groups