Equivariant frame fields on spheres with complementary equivariant complex structures

LetG be a finite group and letM be a unitary representation space ofG. We consider the existence problem of equivariant frame fields on the unit sphereS(M) whose orthogonal complements in the tangent bundleT(S(M)) admitG-equivariant complex structures. Under mild fixed point conditions we give a complete solution for this problem whenG is either ℤ/2ℤ or a finite group of odd order. This article was processed by the author using theLaT_EX style filecljourl from Springer-Verlag.