Differential formes over the projective real space under a general linear group action
It is shown that the only subspaces of the space of \(p\)-forms on the real projective space which are invariant under projective transforms and closed for the \(C^\infty \) topology are the following ones: the zero subspace, the subspace of closed forms, and the space itself. The analogous problem for the sphere is also solved. See also \textit{B. Gruber} and \textit{A. U. Klimyk}, J. Math. Phys. 22, No. 12, 2762-2769 (1981; Zbl 0485.22021), \textit{A. Haefliger} and \textit{L. Banghe}, Lect. Notes Math. 1007, 369-378 (1983; Zbl 0542.58004), \textit{N. R. Wallach}, `Real reductive groups. II.', Boston: Acadmic Press (1992; Zbl 0785.22001), and \textit{R. E. Howe} and \textit{E.-C. Tan}, Bull. Am. Math. Soc., New Ser. 28, No. 1, 1-74 (1993; Zbl 0794.22012).
scientific article; zbMATH DE number 838576