Universal spaces for manifolds equipped with an integral closed \(k\)-form. (English) Zbl 1199.53077

Lê, Hông-Vân

Arch. Math., Brno 43, No. 5, 443-457 (2007).

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.)

Keywords:

closed \(k\)-form; universal space; \(H\)-principle