A taut foliation is a codimension-one foliation 
of an orientable closed manifold 
of dimension 3 for which, for
every foliation leaf 
in the leaf space 
of 
, there is a circle 
transverse
to 
(i.e., a closed loop transverse to the tangent
planes of 
)
which intersects 
.
Taut foliations play a significant role in various aspects of topology and are credited as being one of two major tools (along with incompressible surfaces) responsible for revealing significant topological and geometric information about 3-manifolds (Gabai and Oertel 1989). As such, a considerable amount of research has gone into the study of taut foliations on 3-manifolds. For a co-oriented foliation on such a manifold, every nonclosed foliation leaf meets a closed transversal. Consequently, a foliation without closed foliation leaves is taut. A taut foliation contains no Reeb component. A foliation leaf missed by every closed transversal is a torus bounding a dead-end component. The closed foliation leaves of a co-oriented taut foliation are homologically nontrivial (Calegari 2007).
The remaining characterizations are stated for co-oriented foliations on orientable closed
manifolds of dimension 3. One such result, attributed
by Eliashberg and Thurston to Novikov and Sullivan, says that a foliation 
on a 3-dimensional closed manifold 
is taut if it is different from the product foliation 
on 
with foliation leaves 
, 
, and satisfies any one of the following:
1. Each foliation leaf 
of 
is intersected by a transversal closed curve.
2. There exists a vector field 
on 
which is transversal
to 
and preserves a volume form 
on 
.
3. 
admits a Riemannian metric for which all foliation leaves are minimal
surfaces.
Moreover, a necessary and sufficient condition for tautness of a foliation 
is that 
contain no generalized
Reeb components (Goodman 1975).
