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Article Citation - WoS: 61Citation - Scopus: 64A curvature condition for a twisted product to be a warped product(Springer-verlag, 2001) Fernández-López, M; García-Río, E; Kupeli, DN; Ünal, BIt is shown that a mixed Ricci-flat twisted product semi-Riemannian manifold can be expressed as a warped product semi-Riemannian manifold. Asa consequence, any Einstein twisted product semi-Riemannian manifold is in fact, a warped product serni-Riemannian manifold.Article Citation - WoS: 31Citation - Scopus: 30Characterizing Specific Riemannian Manifolds by Differential Equations(Springer, 2003) Erkekoglu, F; García-Río, E; Kupeli, DN; Ünal, BSome characterizations of certain rank-one symmetric Riemannian manifolds by the existence of nontrivial solutions to certain partial differential equations on Riemannian manifolds are surveyed.Article Citation - WoS: 2Citation - Scopus: 1A Local Analytic Characterization of Schwarzschild Metrics(Elsevier Science Bv, 2003) Fernández-López, M; García-Río, E; Kupeli, DNA local characterization of Schwarzschild metrics is made by showing the space-time is locally a 2 by 2 warped product and admitting a static reference frame on its certain open subsets under some assumptions on the global analytic structure and stress-energy tensor of the space-time, such as, assuming the existence of solutions to certain partial differential equations and the existence of a radiation stress-energy tensor consistent with these solutions on the space-time. (C) 2002 Elsevier Science B.V. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1The Local Mobius Equation and Decomposition Theorems in Riemannian Geometry(Canadian Mathematical Soc, 2002) Fernández-López, M; García-Río, E; Kupeli, DNA partial differential equation, the local Mobius equation, is introduced in Riemannian geometry which completely characterizes the local twisted product structure of a Riemannian manifold. Also the characterizations of warped product and product structures of Riemannian manifolds are made by the local Mobius equation and an additional partial differential equation.Article Citation - WoS: 47Citation - Scopus: 47On a differential equation characterizing Euclidean spheres(Academic Press inc Elsevier Science, 2003) García-Río, E; Kupeli, DN; Ünal, BA characterization of Euclidean spheres out of complete Riemannian manifolds is made by certain vector fields on complete Riemannian manifolds satisfying a partial differential equation on vector fields. (C) 2003 Elsevier Inc. All rights reserved.
