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Proceedings of the London Mathematical Society 2006 93(3):791-816; doi:10.1017/S0024611506015966
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© London Mathematical Society

G-Structures on Spheres

Martin Cadek and Michael Crabb

Department of Algebra and Geometry, Masaryk University Janáckovo nám. 2a, 602 00 Brno, Czech Republic, cadek{at}math.muni.cz
Department of Mathematical Sciences, University of Aberdeen Aberdeen, AB24 3UE, United Kingdom, m.crabb{at}maths.abdn.ac.uk

Received 4 October 2005.

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 -> Gn, where Gn 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 Gn in the fibre bundle Gn -> Gn + 1 -> Gn + 1 / Gn. 2000 Mathematics Subject Classification 55R25, 55R50 (primary), 53C10 (secondary).


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