Non-LTE Abundances of Magnesium, Aluminum and Sulfur in OB Stars Near the Solar Circle

Non-LTE abundances of magnesium, aluminum and sulfur are derived for a sample of 23 low-v \sin i stars belonging to six northern OB associations of the Galactic disk within 1 kpc of the Sun. The abundances are obtained from the fitting of synthetic line profiles to high resolution spectra. A comparison of our results with HII region abundances indicates good agreement for sulfur while the cepheid abundances are higher. The derived abundances of Mg show good overlap with the cepheid results. The aluminum abundances for OB stars are significantly below the cepheid values. But, the OB star results show a dependence with effective temperature and need further investigation. The high Al abundances in the cepheids could be the result of mixing. A discussion of the oxygen abundance in objects near the solar circle suggests that the current mean galactic oxygen abundance in this region is 8.6-8.7 and in agreement with the recently revised oxygen abundance in the solar photosphere. Meaningful comparisons of the absolute S, Al and Mg abundances in OB stars with the Sun must await a reinvestigation of these elements, as well as the meteoritic reference element Si, with 3D hydrodynamical model atmospheres for the Sun. No abundance gradients are found within the limited range in galactocentric distances in the present study. Such variations would be expected only if there were large metallicity gradients in the disk.Comment: 3 figures, accepted for publication in A&A, needs aa.st

Sequences of harmonic maps in the 3-sphere

We define two transforms between non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between non-conformal harmonic maps into the 3-sphere, $H$-surfaces in Euclidean 3-space and almost complex surfaces in the nearly K\"ahler manifold $S^3\times S^3$. As a consequence we can construct sequences of $H$-surfaces and almost complex surfaces.Comment: 14 pages. Second version. The article has been extended and is thoroughly revise

Special classes of three dimensional affine hyperspheres characterized by properties of their cubic form

It is well known that locally strongly convex ane hyperspheres can be determined as solutions of dierential equations of Monge-Ampere type. The global properties of those solutions are well understood. However, due to the nature of the Monge-Ampere equation, not much isknown about local solutions, particularly if the dimension of the hypersurface is greater then 2. By the fundamental theorem, ane hyperspheres are completely determined by their metric h and their dierence tensor K which together build the symmetric cubic form C . Following an idea of Bryant [1],we want toinvestigate ane hyperspheres for which at each point there exist isometries with respect to h preserving this cubic form. The rst non-trivial case is the case that M is 3-dimensional which is also the case which is investigated further in this paper