There are several different definitions of "tautness" for foliations, the most widely know is probably topological tautness, which is specific to codimension one and means that the foliation has a complete closed transversal. Other than that I know that for general codimension there are the concepts of geometrical tautness, which means we can find a Riemannian metric with respect to which all the leaves are minimal submanifolds, and homological tautness, which has a rather technical definition involving certain singular chains.
Geometric and homological tautness are always equivalent, and the three definitions are the same in the codimension one case.
This makes me wonder if there is any set of conditions implying the existence of closed complete transversals for taut foliations in general codimension, like there is in the topological tautness case. I know that we can't hope for the existence of complete transversals in general, because I have examples of transversely symplectic foliation which are geometrically taut and have exact symplectic forms on their normal bundles, so that the existence of a closed transversal would contradict Stoke's Theorem.
I wonder if there are any cases when the existence of such closed transversals is guaranteed, or if anyone can point out any results in this direction. I searched the literature to the best of my abilities but couldn't find anything.
