EQUIVARIANT FRAME FIELDS ON SPHERES WITH COMPLEMENTARY EQUIVARIANT COMPLEX STRUCTURES

Let G be a finite group and let M be a unitary representation space of G. We consider the existence problem of equivariant frame fields on t he unit sphere S(M) whose orthogonal complements in the tangent bundle T(S(M)) admit G-equivariant complex structures. Under mild fixed poin t conditions we give a complete solution for this problem when G is ei ther Z/2Z or a finite group of odd order.