Foliations admitting transverse systems of differential equations
Characteristic classes of multifoliations
Infinitesimal automorphisms of distributions
Infinitesimal automorphisms of some G-structures
On G-foliations
Maximal ideals in Loc (M,F).
Deforming metrics of foliations
Let M be a Riemannian manifold equipped with two complementary orthogonal distributions D and D ⊥. We introduce the conformal flow of the metric restricted to D with the speed proportional to the divergence of the mean curvature vector H, and study the question: When the metrics converge to one for which D enjoys a given geometric property, e.g., is harmonic, or totally geodesic? Our main observation is that this flow is equivalent to the heat flow of the 1-form dual to H, provided the initial 1-form...
Preface
The BIC of a singular foliation defined by an abelian group of isometries
We study the cohomology properties of the singular foliation ℱ determined by an action Φ: G × M → M where the abelian Lie group G preserves a riemannian metric on the compact manifold M. More precisely, we prove that the basic intersection cohomology is finite-dimensional and satisfies the Poincaré duality. This duality includes two well known situations: ∙ Poincaré duality for basic cohomology (the action Φ is almost free). ∙ Poincaré duality for intersection cohomology (the group G is compact...
Foliated G-structures and riemannian foliations.
Le graphe d'un feuilletage admettant un système transverse d'équations differentielles.
Maximal subalgebra in the algebra of foliated vector fields of a Riemannian foliation.
The graph of a totally geodesic foliation
We study the properties of the graph of a totally geodesic foliation. We limit our considerations to basic properties of the graph, and from them we derive several interesting corollaries on the structure of leaves.
Leaves of foliations with a transverse geometric structure of finite type.
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.
Pierrot's theorem for singular Riemannian foliations.
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.
Foliated and associated geometric structures on foliated manifolds
On transverse structures of foliations
On -G-foliations
Top-Dimensional Group of the Basic Intersection Cohomology for Singular Riemannian Foliations
It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an example of a singular isometric flow for which the top-dimensional basic cohomology group is non-trivial, but the basic cohomology does not satisfy...
Transversal biwave maps
In this paper, we prove that the composition of a transversal biwave map and a transversally totally geodesic map is a transversal biwave map. We show that there are biwave maps which are not transversal biwave maps, and there are transversal biwave maps which are not biwave maps either. We prove that if is a transversal biwave map satisfying certain condition, then is a transversal wave map. We finally study the transversal conservation laws of transversal biwave maps.
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