On holomorphic planes

Summary In a manifold, almost complex, Hermitian or Kaehlerian, we shall introduce the notion of the axiom of holomorphic planes and show that a ϕ-connection in such a manifold is given strong restrictions if it satisfies the axiom of holomorphic planes. The main results are formulated in Theorems4.1, 4.2, 5.3 and5.7