Tautness for riemannian foliations on non-compact manifolds

الأصل · EN

For a riemannian foliation F on a closed manifold M, it is known that F is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form κμ (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 Hⁿ(M/F), where n = F. By the Poincaré Duality, this last condition is equivalent to the non-vanishing of the basic twisted cohomology group H⁰κμ(M/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).