G-structures on Spheres
نویسنده
چکیده
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 ρ : G → Gn, where Gn is one of the groups SO(n), SU(n), Sp(n) and G is one of the groups SO(k), SU(k), Sp(k), which reduce the structure group Gn in the fibre bundle Gn → Gn+1 → Gn+1/Gn.
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