Tautness for riemannian foliations on non-compact manifolds

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dc.creatorPrieto, J. I. Royo
dc.creatorSaralegi-Aranguren, M.
dc.creatorWolak, R.
dc.date2005-05-31
dc.date2005-11-19
dc.date.accessioned2026-07-07T09:38:54Z
dc.date.available2026-07-07T09:38:54Z
dc.descriptionFor 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 $κ_μ$ (relatively to a suitable riemannian metric $μ$) 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 Poincaré Duality, this last condition is equivalent to the non-vanishing of the basic twisted cohomology group $H^{^{0}}_{_{κ_μ}}(M/\mathcal{F})$, 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).
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0505675
dc.identifierhttp://arxiv.org/abs/math/0505675
dc.identifierManuscripta math. 126(2008), 177 - 200
dc.identifierdoi:10.1007/s00229-008-0172-0
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160979
dc.subjectDifferential Geometry
dc.subjectAlgebraic Topology
dc.subject57R30
dc.titleTautness for riemannian foliations on non-compact manifolds
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