Geometric interpretation of the Wagner curvature tensor in the case of a manifold with contact metric structure

Considering a manifold $(\varphi,\vec\xi,\eta,X,D)$ with contact metric structure, we introduce the concept of $N$-extended connection (connection on a vector bundle $(D,\pi,X)$), with $N$ an endomorphism of the distribution $D$, and show that the curvature tensor of each $N$-extended connection for a suitably chosen endomorphism $N$ coincides with the Wagner curvature tensor.