Betti numbers and Euler's formula for combinatorial foliations.

Gábor Elek

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Displaying similar documents to “Betti numbers and Euler's formula for combinatorial foliations.”

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A Weitzenböck formula for SL(q)-foliations is derived. Its linear part is a relative trace of the relative curvature operator acting on vector valued forms.

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In this short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation of equivalently the space of leaves of such a foliation is a Satake manifold. A particular attention is paid to transversaly affine foliations. We present several conditions which ensure completeness of such foliations.

Nontaut foliations and isoperimetric constants

Konrad Blachowski (2002)

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We study nontaut codimension one foliations on closed Riemannian manifolds. We find an estimate of some constant derived from the mean curvature function of the leaves of a foliation by some isoperimetric constant of the manifold. Moreover, for foliated 2-tori and the 3-dimensional unit sphere, we find the infimum of the former constants for all nontaut codimension one foliations.