A characterization of harmonic foliations by the volumepreserving property of the normal geodesic flow.
A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas
We construct a two dimensional foliation with dense leaves on the Heisenberg nilmanifold for which smooth leafwise Hodge decomposition does not hold. It is also shown that a certain type of dynamical trace formulas relating periodic orbits with traces on leafwise cohomologies does not hold for arbitrary flows.
A few remarks on the geometry of the space of leaf closures of a Riemannian foliation
The space of the closures of leaves of a Riemannian foliation is a nice topological space, a stratified singular space which can be topologically embedded in for k sufficiently large. In the case of Orbit Like Foliations (OLF) the smooth structure induced by the embedding and the smooth structure defined by basic functions is the same. We study geometric structures adapted to the foliation and present conditions which assure that the given structure descends to the leaf closure space. In Section...
A Fiber bundle theorem.
A finiteness theorem for Riemannian submersions
Given some geometric bounds for the base space and the fibres, there is a finite number of conjugacy classes of Riemannian submersions between compact Riemannian manifolds.
A Foliated Metric Rigidity Theorem for Higher Rank Irreducible Symmetric Spaces.
A note on codimension-1 foliations
A note on generalized flag structures
Generalized flag structures occur naturally in modern geometry. By extending Stefan's well-known statement on generalized foliations we show that such structures admit distinguished charts. Several examples are included.
A spectral estimate for the Dirac operator on Riemannian flows
We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.
A symplectic reduction for pseudo-Riemannian manifolds with compatible almost product structures.
A Weitzenbôck formula for the second fundamental form of a Riemannian foliation
Si considera la seconda forma fondamentale di foliazioni su varietà riemanniane e si ottiene una formula per il laplaciano - Se ne deducono alcune implicazioni per foliazioni su varietà a curvatura costante.
Actions de groupes sur les -variétés non séparées et feuilletages de codimension un
Algebroid nature of the characteristic classes of flat bundles
The following two homotopic notions are important in many domains of differential geometry: - homotopic homomorphisms between principal bundles (and between other objects), - homotopic subbundles. They play a role, for example, in many fundamental problems of characteristic classes. It turns out that both these notions can be - in a natural way - expressed in the language of Lie algebroids. Moreover, the characteristic homomorphisms of principal bundles (the Chern-Weil homomorphism [K4], or the...
An analog of the Vaisman-Molino cohomology for manifolds modelled on some types of modules over Weil algebras and its application.
An integral formula for a Riemannian manifold with two orthogonal complementary distributions
An invariant of nonpositively curved contact manifolds
We define an invariant of contact structures and foliations (on Riemannian manifolds of nonpositive sectional curvature) which is upper semi-continuous with respect to deformations and thus gives an obstruction to the topology of foliations which can be approximated by isotopies of a given contact structure.