GLOBAL HYPOELLIPTICITY, GLOBAL SOLVABILITY AND NORMAL FORM FOR A CLASS OF REAL VECTOR FIELDS ON A TORUS AND APPLICATION

The main purpose of this paper is to present a class of real vector fields defined on a torus for which the concepts of global hypoellipticity and global smooth solvability are equivalent. Furthermore, such a vector field is globally hypoelliptic if and only if its adjoint is globally hypoelliptic, and therefore we can reduce it to its normal form. As an application, we study global C-infinity solvability for certain classes of sub-Laplacians.