We compute future timelike and nonspacelike reachable sets from the origin for a class of contact sub-Lorentzian metrics on ℝ³. Then we construct non-smooth (and therefore non-Hamiltonian) null geodesics for these metrics. As a consequence we deduce that the sub-Lorentzian distance from the origin is continuous at points belonging to the boundary of the reachable set.

In this paper we classify real hypersurfaces with constant totally real bisectional curvature in a non flat complex space form $M_m\left(c\right)$, $c\ne 0$ as those which have constant holomorphic sectional curvature given in [6] and [13] or constant totally real sectional curvature given in [11].

We define a procedure of reduction of locally conformal symplectic structures. We find a necessary and sufficient condition for this reduction to hold in terms of a special kind of de Rham cohomology class (tangent to the characteristic foliation) of the Lee form.

This paper concerns projectively Anosov flows ${\phi }^t$ with smooth stable and unstable foliations ${ℱ}^s$ and ${ℱ}^u$ on a Seifert manifold $M$. We show that if the foliation ${ℱ}^s$ or ${ℱ}^u$ contains a compact leaf, then the flow ${\phi }^t$ is decomposed into a finite union of models which are defined on $T^2\times I$ and bounded by compact leaves, and therefore the manifold $M$ is homeomorphic to the 3-torus. In the proof, we also obtain a theorem which classifies codimension one foliations on Seifert manifolds with compact leaves which are incompressible...

A flag on a manifold $M$ is an increasing sequence of foliations $\left({ℱ}_1,\cdots ,{ℱ}_p\right)$ on this manifold, where for each $i$, $dim{ℱ}_i=i$. The aim of this paper is to etablish that any flag of riemannian foliations $𝒟=$$\left({ℱ}_1,\right)$

In this paper, we consider a Riemannian foliation that admits a nontrivial parallel or harmonic basic form. We estimate the norm of the O’Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.

Every open manifold $L$ of dimension greater than one has complete Riemannian metrics $g$ with bounded geometry such that $(L,g)$ is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the local geometry of $(L,g)$ suffice to make it quasi-isometric to a leaf of such a foliation. We introduce the ‘bounded homology property’, a semi-local property of $(L,g)$ that is necessary for it to be a leaf in a compact manifold in codimension one, up to quasi-isometry. An essential...