A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas

Christopher Deninger; Wilhelm Singhof

Displaying similar documents to “A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas”

On riemannian foliations with minimal leaves

Jesús A. Alvarez Lopez (1990)

Annales de l'institut Fourier

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For a Riemannian foliation, the topology of the corresponding spectral sequence is used to characterize the existence of a bundle-like metric such that the leaves are minimal submanifolds. When the codimension is $\leq 2$ , a simple characterization of this geometrical property is proved.

De Rham-Hodge Theory for Riemannian Foliations.

F.W. Kamber, P. Tondeur (1987)

Mathematische Annalen

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Some properties of foliations

Richard Sacksteder (1964)

Annales de l'institut Fourier

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Pierrot's theorem for singular Riemannian foliations.

Robert A. Wolak (1994)

Publicacions Matemàtiques

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Let F be a singular Riemannian foliation on a compact connected Riemannian manifold M. We demonstrate that global foliated vector fields generate a distribution tangent to the strata defined by the closures of leaves of F and which, in each stratum, is transverse to these closures of leaves.

Projectively Anosov flows with differentiable (un)stable foliations

Takeo Noda (2000)

Annales de l'institut Fourier

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We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on $T^{2}$ which can be extended on a neighbourhood of $T^{2}$ into a projectively Anosov flow so that $T^{2}$ is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on $T^{3}$ . In this case, the only flows on $T^{2}$ which...

De Rham decomposition theorems for foliated manifolds

Robert A. Blumenthal, James J. Hebda (1983)

Annales de l'institut Fourier

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We prove that if $M$ is a complete simply connected Riemannian manifold and $F$ is a totally geodesic foliation of $M$ with integrable normal bundle, then $M$ is topologically a product and the two foliations are the product foliations. We also prove a decomposition theorem for Riemannian foliations and a structure theorem for Riemannian foliations with recurrent curvature.