The notion of contact triad connection on contact triads (Q, λ, J_ξ) was introduced by Wang and the present author in early 2010's from scratch as the contact analog to the canonical connection of an almost Kähler manifolds. The connection facilitates the study of analysis of the contact instanton equation which ranges from local elliptic priori estimates, for both the interior OW2, OW3 and the boundary OY, to the generic perturbation theory of the asymptotic operators KO, which also encompasses the case of pseudoholomorphic curves on noncompact symplectic manifolds with cylindrical ends OK. The main purpose of the present paper is to give a simpler and more canonical construction of the contact triad connection by first giving its characterization in terms of the associated almost contact structure and then providing its construction using the almost contact moving frame in the framework of contact geometry.
Yong‐Geun Oh (Wed,) studied this question.