no. 3
Decomposition in the large of two-forms of constant rank
Annales de l'Institut Fourier, Tome 24 (1974) no. 3, pp. 317-335.

Le but de ce travail est de trouver les conditions nécessaires et suffisantes pour la décomposition globale d’une 2-forme extérieure w, de rang constant 2s, sur un espace fibré vectoriel E, comme une somme

w = y 1 ∧ y s + 1 + ⋯ + y s ∧ y 2 s .

La théorie générale est appliquée aux espaces de dimensions inférieures comme les sphères, et les espaces projectifs réels et complexes.

The purpose of this paper is to find necessary and sufficient conditions for globally-decomposing an exterior 2-form w, of constant rank 2s, on a vector-bundle E, as a sum :

w = y 1 ∧ y s + 1 + ⋯ + y s ∧ y 2 s .

The general theory is applied to low dimensional manifolds, spheres, real and complex projective spaces.

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     author = {Dibag, Ibrahim},
     title = {Decomposition in the large of two-forms of constant rank},
     journal = {Annales de l'Institut Fourier},
     pages = {317--335},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {24},
     number = {3},
     year = {1974},
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     zbl = {0287.58001},
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Dibag, Ibrahim. Decomposition in the large of two-forms of constant rank. Annales de l'Institut Fourier, Tome 24 (1974) no. 3, pp. 317-335. doi : 10.5802/aif.529. http://www.numdam.org/articles/10.5802/aif.529/

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