1 research outputs found
Tautness for riemannian foliations on non-compact manifolds
For a riemannian foliation on a closed manifold , it is
known that is taut (i.e. the leaves are minimal submanifolds) if
and only if the (tautness) class defined by the mean curvature form
(relatively to a suitable riemannian metric ) is zero. In the
transversally orientable case, tautness is equivalent to the non-vanishing of
the top basic cohomology group , where n = \codim
\mathcal{F}. By the Poincar\'e Duality, this last condition is equivalent to
the non-vanishing of the basic twisted cohomology group
, when is oriented. When is
not compact, the tautness class is not even defined in general. In this work,
we recover the previous study and results for a particular case of riemannian
foliations on non compact manifolds: the regular part of a singular riemannian
foliation on a compact manifold (CERF).Comment: 18 page