Manifolds admitting stable forms. (English) Zbl 1212.53051

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.


53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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