Leafwise Dolbeault cohomology of certain complex foliations (Q978575)

The authors compute the leafwise Dolbeault cohomology (obstruction to solve the Cauchy-Riemann problem along the leaves of a complex foliation) for two classes of complex foliations: i) the two dimensional complex affine Reeb foliations on the Hopf \(5\)-manifold; ii) complex foliations on the hyperbolic torus (fibration over the circle whose fibre is the \( n\)-dimensional torus and its monodromy is a hyperbolic and diagonalizable matrix all of whose eigenvalues are real and positive) obtained by locally free actions of the real affine Lie group.