  A generalization of the Hartogs theorem is proved for a class of Tubes
structures. We assume that the intervening commutative Lie algebra admits at
least a number of globally solvable generators greater or equal to the
structure codimension. We give necessary and sufficient conditions for the
first cohomological group with compact support to be trivial. A such global
result was previously obtained only when the supporting manifold was the
Euclidean space. Further but canonical work is need to recover the Bochner
extension theorem.
