On transverse structures of foliations
On -G-foliations
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
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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