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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.

##### MSC:
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
##### Keywords:
stable forms; automorphism groups
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