LOCAL INTEGRABILITY OF MIZOHATA STRUCTURES

In this work we study the local integrability of strongly pseudoconvex Mizohata structures of rank n > 2 (and co-rank 1). These structures a re locally generated in an appropriate coordinate system (t1, ... , t( n), x) by flat perturbations of Mizohata vector fields M(j) = partial derivative/partial derivative t(j) - it(j)partial derivative/partial d erivative x, j = 1, . . . , n . For this, we first prove the global in tegrability of small perturbations of the structure generated by parti al derivative/partial-derivative zBAR + sigma1 partial derivative/part ial derivative theta(n-1 + sigma(j)partial derivative/partial derivati ve(z), j = 2, ... , n , defined over a manifold C x S , where S is sim ply connected.