Use este identificador para citar ou linkar para este item: http://www.repositorio.ufc.br/handle/riufc/18693
Título: Uniqueness of quasi-einstein metrics on 3-dimensional homogeneous manifolds
Título em inglês: Uniqueness of quasi-einstein metrics on 3-dimensional homogeneous manifolds
Autor(es): Barros, Abdenago Alves de
Ribeiro Junior, Ernani de Sousa
Silva Filho, J
Palavras-chave: Einstein metrics
quasi-Einstein metrics
Data do documento: 2014
Editor: Differential Geometry and its Applications
Citação: BARROS, A.; RIBEIRO JR, E.; SILVA FILHO, J. (2014)
Abstract: The purpose of this article is to study the existence and uniqueness of quasi-Einstein structures on 3-dimensional homogeneous Riemannian manifolds. To this end,we use the eight model geometries for 3-dimensional manifolds identified by Thurston. First, we present here a complete description of quasi-Einstein metrics on 3-dimensional homogeneous manifolds with isometry group of dimension 4. In addition, we shall show the absence of such gradient structure on Sol3, which has 3-dimensional isometry group. Moreover, we prove that Berger’s spheres carry a non-trivial quasi-Einstein structure with non gradient associated vector field, this shows that a theorem due to Perelman can not be extend to quasi-Einstein metrics. Finally, we prove that a 3-dimensional homogeneous manifold carrying a gradient quasi-Einstein structure is either Einstein or H2 × R.
Descrição: BARROS, A.; RIBEIRO JR., E.; SILVA FILHO, J. Uniqueness of quasi-einstein metrics on 3-dimensional homogeneous manifolds. Differential Geometry and its Applications, v. 35, p. 60-73, 2014.
URI: http://www.repositorio.ufc.br/handle/riufc/18693
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