Differentiable solutions of algebraic equations on manifolds

Abstract

Introduction. Yano [7] introduced the notion of an f-structure, which is a non-null (1,1) tensor field / of constant rank r on a C manifold of dimension r+m, satisfying / 3 -f/-0. An almost complex and an almost contact structure are particular cases of an /-structure the existence of an /-structure being equivalent to a reduction of the structural group of the tangent bundle to U(r/2)xO(m). They were studied by various authors ([1], [2], [6], etc.) with particular focus on the case of globally framed structures Extending the concept of an /-structure, Goldberg and Yano [3] introduced the notion of a polynomial structure on a manifold.