Georgiou N.,Rua do Matao |
Guilfoyle B.,Institute of Technology, Tralee
Journal of Geometry and Physics | Year: 2014
We investigate the geometric properties of marginally trapped surfaces (surfaces which have null mean curvature vector) in the spaces of oriented geodesics of Euclidean 3-space and hyperbolic 3-space, endowed with their canonical neutral Kaehler structures. We prove that every rank one surface in these four manifolds is marginally trapped. In the Euclidean case we show that Lagrangian rotationally symmetric sections are marginally trapped and construct an explicit family of marginally trapped Lagrangian tori. In the hyperbolic case we explore the relationship between marginally trapped and Weingarten surfaces, and construct examples of marginally trapped surfaces with various properties. © 2014 Elsevier B.V.
Mantovani M.S.M.,Rua do Matao |
Louro V.H.A.,Rua do Matao |
Ribeiro V.B.,Rua do Matao |
Requejo H.S.,Rua Barao do Triunfo 550 |
Santos R.d.,Rua do Matao
Geophysical Prospecting | Year: 2015
The Catalão I alkaline-carbonatite complex, which is located in Central Brazil, is one of the main producers of niobium and phosphates in the world. It has been intensely studied geologically and geochemically for its economic potential. This work presents a geophysical analysis over this complex, identifying its behaviour in the subsurface and in portions that have not been explored yet. Different geophysical methods and techniques were applied to achieve the most reliable results possible: at the surface, through radiometric, geological, and topographic data, and at depth, by geological, magnetic, and gravimetric data. The analysis was successfully completed with inversions of gravity and magnetic data that resulted in quite similar models, both in volume and shape. Their density and magnetic susceptibility contrasts were consistent with the expected dunite-pyroxenite lithology from the original mafic intrusion and indicated (by exclusion) the volume of the carbonatite body, which along with the known contents of phosphates and niobium allowed an indirect estimate of the reserves and resources of the complex. © 2015 European Association of Geoscientists & Engineers.