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Universal spaces for manifolds equipped with an integral closed $$k$$-form. (English) Zbl 1199.53077
Summary: We prove that any integral closed $$k$$-form $$\phi ^k$$, $$k\geq 3$$, on a m-dimensional manifold $$M^m$$, $$m \geq k$$, is the restriction of a universal closed $$k$$-form $$h^k$$ on a universal manifold $$U^{d(m,k)}$$ as a result of an embedding of $$M^m$$ to $$U^{d(m,k)}$$.
MSC:
 53C10 $$G$$-structures 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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