$G$- structures on spheres

• Autores: Martin Cadek, Michael J. Crabb
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 93, Nº 3, 2006, págs. 791-816
• Idioma: inglés
• DOI: 10.1017/s0024611506015966
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• Resumen

  • A generalization of classical theorems on the existence of sections of real, complex and quaternionic Stiefel manifolds over spheres is proved. We obtain a complete list of Lie group homomorphisms $\rho : G \to G_n$, where $G_n$ is one of the groups $SO(n)$, $SU(n)$ or $Sp(n)$ and $G$ is one of the groups $SO(k)$, $SU(k)$ or $Sp(k)$, which reduce the structure group $G_n$ in the fibre bundle $G_n \to G_{n + 1} \to G_{n + 1} / G_n$.