Almost complex structures on the tensor bundles

Abstract EN

Let M be an n −dimensional differentiable manifold of class C∞ , Tpq (M) its tensor bundles of type ( p, q) .

It is well known that the tensor bundle of type (1, q) of M admits an almost complex structure on the pure cross-section, if M admits an almost complex structure.

The main purpose of this paper is to investigate a similar problem for tensor bundles Tpq (M) of type (p, q) , p > 1 .

We prove that if a manifold M admits an almost complex structure ϕ , then so does Tpq (M), p > 1 on the pure cross-section provided ϕ is integrable.

The proofs depend on some generalizations of the notions of lifting derivations.