Tautness for riemannian foliations on non-compact manifolds

Details Tautness for riemannian foliations on non-compact manifolds Tautness for riemannian foliations on non-compact manifolds

2005-05-31

arxiv.org/abs/math/0505675v2

Manuscripta math. 126(2008), 177 - 200

Mathematics

Differential Geometry

18 pages

Scientific paper

10.1007/s00229-008-0172-0

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $\kappa_\mu$ (relatively to a suitable riemannian metric $\mu$) is zero. In the transversally orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group $H^{^{n}}(M/\mathcal{F})$, 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 $H^{^{0}}_{_{\kappa_\mu}}(M/\mathcal{F})$, when $M$ is oriented. When $M$ 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).

Affiliated with

Also associated with

No associations

Rating

Tautness for riemannian foliations on non-compact manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Tautness for riemannian foliations on non-compact manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tautness for riemannian foliations on non-compact manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-455710