
Papers  Structures related to parallelizations 



Structures related to parallelizations
Abstract
A classical theorem of Kervaire states that products of spheres are
parallelizable if and only if at least one of the factors has odd
dimension.
The versor field given by
the complex multiplication on the odddimensional factor gives
explicit parallelizations B and P.
In this paper I use B and P to obtain orthogonal and symmetric orbits
of B and Pinvariant Gstructures on S^{m}×S^{n},
where G=U(m+n)/2, Sp(m+n)/4, G_{2}, Spin(7),
Spin(9). This approach leads to an alternative description of
classical structures as well as to new structures on products of
spheres.






