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Papers - Structures related to parallelizations
pdf ps Structures related to parallelizations

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 odd-dimensional factor gives explicit parallelizations B and P. In this paper I use B and P to obtain orthogonal and symmetric orbits of B and P-invariant G-structures on Sm×Sn, where G=U(m+n)/2, Sp(m+n)/4, G2, Spin(7), Spin(9). This approach leads to an alternative description of classical structures as well as to new structures on products of spheres.