The space of transversely projective structures on a transversely holomorphic foliation is described. Some applications are given.

New examples of harmonic unit vector fields on hyperbolic 3-space are constructed by exploiting the reduction of symmetry arising from the foliation by horospheres. This is compared and contrasted with the analogous construction in Euclidean 3-space, using a foliation by planes, which produces some new examples of harmonic maps from 3-dimensional Euclidean domains to the 2-sphere. Finally, the ...

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta inva...

Let X be a C’ vectorfield on S* = {(x, y, z) E iw3: x2 +y2 + z2 = 1 } such that no open subset of S* is the union of closed orbits of X. If X has only a finite number of singular orbits and satisfies one additional condition, then it is shown that X is topologically equivalent to a polynomial vectorfield. A corollary is that a foliation 9 of the plane is topologically equivalent to a foliation ...

We study the Hochschild homology groups of the algebra of complete symbols on a foliated manifold (M, F ). The first step is to relate these groups to the Poisson homology of (M, F ) and of other related foliated manifolds. We then establish several general properties of the Poisson homology groups of foliated manifolds. As an example, we completely determine these Hochschild homology groups fo...

Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in "horizon" i.e., a smooth 3-surface foliated by marginally outer trapped slices which lie in the leaves of the given foliation. We also show that under rather weak energy conditions this horizon must be either achronal or s...