Corner manifolds

The aim of this paper is two-fold. First, the study of $C_{12}$-structure (called by us corner structure) is extended to the general case without any condition, unlike our previous papers (see, \cite{BB, BG2, BG, BBB}). Second, starting from a $C_{12}$-structure which is not normal, we construct Trans-Sasakian structures which are normal. Class of examples are given.