On the relative CR structure (Q1108419)

Let \(\bar M\) be a compact complex manifold with boundary \(M_ 0\) and let \(\bar N\) be a closed submanifold of \(\bar M\) with boundary \(N_ 0\). The author considers the extension problem of deformations of relative CR structure on \((M_ 0,N_ 0)\) to deformations of relative complex structure on \((\bar M,\bar N)\). He obtains, under some conditions, the extendability of deformations. He announces the existence of a versal family of deformations of the relative complex structure of \((\bar M,\bar N)\) leaving the relative CR structure on \((M_ 0,N_ 0)\) fixed.