Gallot-Tanno Theorem for closed incomplete pseudo-Riemannian manifolds and applications

We extend the Gallot-Tanno Theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over a manifold admits a parallel symmetric $(0,2)-$tensor then it is Riemannian. Applications of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics and to the projective Obata conjecture are given. We also apply our result to show that the holonomy group of a closed $(O(p+1,q),S^{p,q})$-manifold does not preserve any nondegenerate splitting of $\R^{p+1,q}$.Comment: minor correction

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

Conformal proper times according to the Woodhouse causal axiomatics of relativistic spacetimes

On the basis of the Woodhouse causal axiomatics, we show that conformal proper times and an extra variable in addition to those of space and time, precisely and physically identified from experimental examples, together give a physical justification for the `chronometric hypothesis' of general relativity. Indeed, we show that, with a lack of these latter two ingredients, no clock paradox solution exists in which the clock and message functions are solely at the origin of the asymmetry. These proper times originate from a given conformal structure of the spacetime when ascribing different compatible projective structures to each Woodhouse particle, and then, each defines a specific Weylian sheaf structure. In addition, the proper time parameterizations, as two point functions, cannot be defined irrespective of the processes in the relative changes of physical characteristics. These processes are included via path-dependent conformal scale factors, which act like sockets for any kind of physical interaction and also represent the values of the variable associated with the extra dimension. As such, the differential aging differs far beyond the first and second clock effects in Weyl geometries, with the latter finally appearing to not be suitable.Comment: 25 pages, 2 figure

On the affine group of a normal homogeneous manifold

A very important class of homogeneous Riemannian manifolds are the so-called normal homogeneous spaces, which have associated a canonical connection. In this work we obtain geometrically the (connected component of the) group of affine transformations with respect to the canonical connection for a normal homogeneous space. The naturally reductive case is also treated. This completes the geometric calculation of the isometry group of naturally reductive spaces. In addition, we prove that for normal homogeneous spaces the set of fixed points of the full isotropy is a torus. As an application of our results it follows that the holonomy group of a homogeneous fibration is contained in the group of (canonically) affine transformations of the fibers, in particular this holonomy group is a Lie group (this is a result of Guijarro and Walschap).Comment: Final version to appear in Ann. Global Anal. Geom

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

Etude des efforts et de la température de coupe lors de tournage dur de l’acier AISI 52100 par un outil CBN

Dans ce travail nous présentons les résultats théoriques et expérimentaux d’une étude dynamique de la coupe des métaux concernant la mesure des efforts et la température de coupe lors de l’usinage e l’acier à roulement AISI 52100 (60HRC) avec un outil en nitrure de bore cubique CBN 7020. Cette étude, basé sur des essais unifactoriel et multifactorielle (vitesse de coupe, avance et la profondeur de passe) permis la mise en évidence de l’influence des conditions de coupe sur les composantes de l’effort de coupe. Le traitement des résultats obtenus a permis la détermination des différents modèles qui expriment la relation entre les paramètres d’usinage étudiés et les composantes de l’effort de coupe. Nous nous somme également intéressés à l’étude de l’influence de l’usure en dépouille de la partie active de l’outil sur l’évolution des efforts de coupe permettant la proposition d’une relation puissance entre l’effort de coupe et l’usure puisque ces deux paramètres s’influencent mutuellement. Enfin, une analyse des différents résultats obtenus été effectuée.Mots clés: Efforts de coupe; pression spécifique de coupe; usinage dur; CBN; conditions de coupe. In the present work, theoretical and experimental results of dynamics study of metal cutting are presented. This investigation is concerned with the cutting force and temperature measurement during machining of hardened bearing steel AISI 52100 using a Cubic Boron Nitride tool CBN7020. The experimental tests based on both unifatorial and multifactirial methods whose parameters are cutting speed, feed rate and depth of cut led to the determination of the cutting conditions effects on cutting force components. The treatment of the results obtained allowed us the deduction of various models, which express the relation between the studied parameters of machining and the cutting force components. A study of the influence of the flank wear on the evolution of cutting force has also been carried out in order to develop a power relation between the cutting force and the flank wear. Finally, an analysis of the different obtained results has been made.Keywords: Cutting force; Cutting specific pressure; hard machining; CBN; cutting conditions