Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2010. / Submitted by Albânia Cézar de Melo (albania@bce.unb.br) on 2011-05-18T14:09:38Z
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2010_BiankaCarneiroLeandro.pdf: 409098 bytes, checksum: 18adb739fc0294fc9cfca6e7913914af (MD5) / Consideramos o espaço pseudo-Euclidiano (Rn, g), com coordenadas x = (x1, ..., xn), n _ 3, e gij = _ij"i, "i = ±1. Seja T um tensor simétrico de ordem 2, definido por
T = nXi,j=1 "jFij(xk)dxi dxj , onde k ´e fixo, "jFij(xk) = "iFji(xk), 8i, j tais que i 6= j e
para j0 fixo, Fij(xk) = cij , 8i, j tais que i, j, j0 s˜ao distintos, com cij 2 R. Além disso,
assumimos que existem um intervalo aberto I _ R e l0 6= j0 tais que F0 l0j0(xk) 6= 0,
8xk 2 I. Obtemos condições necessrias e suficientes para que tal tensor admita
métrica ¯g, conforme a g, que resolva a equação do tensor de Ricci, Ric ¯g = T. _________________________________________________________________________________ ABSTRACT / We consider the pseudo-Euclidean space (Rn, g), with coordinates x = (x1, ..., xn), n _ 3, and gij = _ij"i. Let T be a symmetric tensor of order 2, defined by T = nXi,j=1 "jFij(xk)dxidxj , where k is fixed, "jFij(xk) = "iFji(xk), 8i, j such that i 6= j and for j0 fixed, Fij(xk) = cij , 8i, j such that i, j, j0 are distinct, with cij 2 R. Moreover, we assume that there is an open interval I _ R and l0 6= j0 such that F0 l0j0(xk) 6= 0, 8xk 2 I. We provide necessary and sufficient conditions for such a tensor to admit a metric ¯g, conformal to g, that solves the Ricci tensor equation, Ric ¯g = T.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.unb.br:10482/8043 |
| Date | 22 September 2010 |
| Creators | Leandro, Bianka Carneiro |
| Contributors | Tenenblat, Keti |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Source | reponame:Repositório Institucional da UnB, instname:Universidade de Brasília, instacron:UNB |
| Rights | info:eu-repo/semantics/openAccess |
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