On the General Theory of Differentiable Manifolds with Almost Tangent Structure

Abstract

Some of the most important G-Structures of the first kind [1] are those defined by linear operators satisfying algebraic relations. If the linear operator J acting on the complexified space of a differentiable manifold V satisfies a relation of the formwhere I is the identity operator, the manifold has an almost complex structure ([2] [3]). The structures defined byare the almost product structures ([3] [4]).