Topological canal foliations

Regular canal surfaces of R-3 or S-3 admit foliations by circles: the characteristic circles of the envelope. In order to build a foliation of S3 with leaves being canal surfaces, one has to relax the condition ``canal'' a little (''weak canal condition'') in order to accept isolated umbilics. Here, we define a topological condition which generalizes this ``weak canal'' condition imposed on leaves, and classify the foliations of compact orientable 3-manifolds we can obtain this way.