Browsing by Author "Kupeli, DN"

Now showing 1 - 6 of 6

Citation - WoS: 31
Citation - Scopus: 30
Characterizing Specific Riemannian Manifolds by Differential Equations
(Springer, 2003) Erkekoglu, F; García-Río, E; Kupeli, DN; Ünal, B
Some characterizations of certain rank-one symmetric Riemannian manifolds by the existence of nontrivial solutions to certain partial differential equations on Riemannian manifolds are surveyed.
Citation - WoS: 61
Citation - Scopus: 64
A curvature condition for a twisted product to be a warped product
(Springer-verlag, 2001) Fernández-López, M; García-Río, E; Kupeli, DN; Ünal, B
It 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.
Citation - WoS: 1
The Generalized Divergence Theorem and Its Application To Harmonic Maps
(Pergamon-elsevier Science Ltd, 2001) García-Río, E; Kupeli, DN
A survey of divergence theorems in semi-Riemannian geometry is made. The generalization of a divergence theorem to vector fields along a map is given in semi-Riemannian geometry and an application of it is made in Riemannian geometry to obtain some sufficient conditions for a map to be harmonic.
Citation - WoS: 2
Citation - Scopus: 1
A Local Analytic Characterization of Schwarzschild Metrics
(Elsevier Science Bv, 2003) Fernández-López, M; García-Río, E; Kupeli, DN
A 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.
Citation - WoS: 1
Citation - Scopus: 1
The Local Mobius Equation and Decomposition Theorems in Riemannian Geometry
(Canadian Mathematical Soc, 2002) Fernández-López, M; García-Río, E; Kupeli, DN
A 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.
Citation - WoS: 47
Citation - Scopus: 47
On a differential equation characterizing Euclidean spheres
(Academic Press inc Elsevier Science, 2003) García-Río, E; Kupeli, DN; Ünal, B
A 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.