  This article describes the following results which relate to each other; i)
convergence of high dimensional contact structure to codimension one foliation
with Reeb component, ii) relation between Nil-type and Sol-type contact
submanifolds of S^5, iii) definition of convex Thurston-Bennequin inequality,
and iv) generalization of Lutz twist via convex hypersurface theory. The other
article concerning non-convex hypersurfaces is included as an appendix.
