Leafwise Holomorphic Functions

It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property holds in the setting of holomorphically foliated spaces

Cosmological time versus CMC time I: Flat spacetimes

This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension $n\geq 3$ with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes admit a globally defined constant mean curvature time function precisely when they are causally incomplete. The proof, which is based on using the level sets of the cosmological time function as barriers, is conceptually simple and will provide the basis for future work on constant mean curvature time functions in general constant curvature spacetimes, as well for an analysis of the asymptotics of constant mean foliations

Protective effect of Atriplex halimus extract against benzene-induced haematotoxicity in rats

Benzen (BZ) is a ubiquitous environmental pollutant with a toxic effect mainly aimed at the hematopoietic­ and immune systems. Atriplex halimus L. (Amaranthaceae) is a Mediterranean halophytic shrub traditionally used in North Africa as medicinal plant for several therapeutic uses. The present study aimed to estimate the preventive and curative effects of Atriplex halimus L. (Ah) aqueous extract against BZ-induced hematotoxici­ty in rats. Analysis of the extract by the method of LC-MS revealed the presence of 7 vitamins, among which vitamin C content was the highest. Adult rats were divided into five groups as follow: Group 1 received water (control); Group 2 received orally Ah aqueous extract (200 mg/kg) 3 days/week for 15 weeks; Group 3 received BZ (100 mg/kg b.w) daily in drinking water for 15 weeks; Group 4 received concomitantly BZ (100 mg/kg) and preventive treatment with Ah (200 mg/kg) for 15 weeks (AhP+BZ); Group 5 first received BZ (100 mg/kg) for 11 weeks and then curative treatment with Ah extract (300 mg/kg) daily for 30 days (BZ+AhC). It was shown that sub-chronic exposure to benzene induced leukopenia, lymphocytopenia, granulocytopenia and massive degeneration of the bone marrow tissue. The level of GSH and activity of GST and CAT were significantly lowered and the level of MDA was increased in the blood and bone marrow in rats of BZ-intoxicated group compared to the control rats. Administration of Ah extract recovered the bone marrow structure, dramatically decreased MDA content and increased GSH and CAT activity and GST level in the blood and bone marrow as compared with the indices in BZ-treated group. These observations demonstrate that curative and, to a lesser extent, preventive treatment with Atriplex halimus extract have therapeutic potential against hematotoxicity induced by benzene

Finsler Conformal Lichnerowicz-Obata conjecture

We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric.Comment: 13 pages, 2 figures; the new version has only minor changes with respect to v1, and is the version that will be published in Annales de L'Institut Fourie

Notes on a paper of Mess

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.Comment: 26 page

Tightness in contact metric 3-manifolds

This paper begins the study of relations between Riemannian geometry and global properties of contact structures on 3-manifolds. In particular we prove an analog of the sphere theorem from Riemannian geometry in the setting of contact geometry. Specifically, if a given three dimensional contact manifold (M,\xi) admits a complete compatible Riemannian metric of positive 4/9-pinched curvature then the underlying contact structure \xi is tight; in particular, the contact structure pulled back to the universal cover is the standard contact structure on S^3. We also describe geometric conditions in dimension three for \xi to be universally tight in the nonpositive curvature setting.Comment: 29 pages. Added the sphere theorem, removed high dimensional material and an alternate approach to the three dimensional tightness radius estimate

Feuilletages géodésiques des variétés localement symétriques

AbstractWe prove here that a hyperbolic manifold of finite volume (not necessarily complete!) does not possess a locally Lipschitz foliation with totally geodesic and complete leaves.RésuméOn démontre ici qu'une variété hyperbolique de volume fini (pas nécessairement complète!) n'admet pas de feuilletage localement Lipschitz, dont les feuilles sont totalement géodésiques et complètes