Browsing by Author "Dobarro, F."
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Item Open Access About curvature, conformal metrics and warped products(Institute of Physics Publishing Ltd., 2007) Dobarro, F.; Ünal, B.We consider the curvature of a family of warped products of two pseduo-Riemannian manifolds (B, gB) and (F, gF) furnished with metrics of the form c2gB ⊕ w2g F and, in particular, of the type w2μgB ⊕ w2gF, where c, w:B → (0, ∞) are smooth functions and μ is a real parameter. We obtain suitable expressions for the Ricci tensor and scalar curvature of such products that allow us to establish results about the existence of Einstein or constant scalar curvature structures in these categories. If (B, gB) is Riemannian, the latter question involves nonlinear elliptic partial differential equations with concave-convex nonlinearities and singular partial differential equations of the Lichnerowicz-York-type among others. © 2007 IOP Publishing Ltd.Item Open Access Characterizing killing vector fields of standard static space-times(Elsevier, 2012) Dobarro, F.; Ünal, B.We provide a global characterization of the Killing vector fields of a standard static space-time by a system of partial differential equations. By studying this system, we determine all the Killing vector fields in the same framework when the Riemannian part is compact. Furthermore, we deal with the characterization of Killing vector fields with zero curl on a standard static space-time. © 2011 Elsevier B.V..Item Open Access Hessian Tensor and standard static space-times(2008) Dobarro, F.; Ünal, Bülent; Scherfner, M.; Plaue, M.In this brief survey, we will remark the interaction among the Hessian tensor on a semi-Riemannian manifold and some of the several questions in Lorentzian (and also in semi-Riemannian) geometry where this 2-covariant tensor is involved. In particular, we deal with the characterization of Killing vector fields and the study of a set of consequences of energy conditions in the framework of standard static space-times.Item Open Access Implications of energy conditions on standard static space-times(Pergamon Press, 2009) Dobarro, F.; Ünal, B.In the framework of standard static space-times, we state a family of sufficient or necessary conditions for a set of physically reasonable energy and convergence conditions in relativity and related theories. We concentrate our study on questions about the sub-harmonicity of the warping function, the scalar curvature map, conformal hyperbolicity, conjugate points and the time-like diameter of this class of space-times. © 2009 Elsevier Ltd. All rights reserved.