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

Abstract

Considering a manifold (φ, ξ, η, g, X, D) with contact metric structure, we introduce the concept of N-extended connection (connection on a vector bundle (D, π,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.