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The prescribed curvature problem in dimension four.

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Muñoz Masqué, Jaime and Pozo Coronado, Luis Miguel and Sánchez Rodríguez, I. (2009) The prescribed curvature problem in dimension four. Journal de Mathématiques Pures et Appliquées, 92 . pp. 599-612. ISSN 0021-7824

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Official URL: http://www.sciencedirect.com/science/article/pii/S0021782409001317


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Abstract

Necessary and sufficient conditions for a g-valued differential 2-form on a 4-dimensional manifold to be, locally, a curvature; form, are given. The dimension four is exceptional for the problem of prescribed curvature as, in this dimension, Bianchi's identities can be eliminated for a large class of Lie algebras, including semisimple algebras. Hence, the curvature forms are characterized as the solutions to a second-order partial differential system, which is proved to be formally integrable.


Item Type:Article
Uncontrolled Keywords:Bianchi identity; Curvature form; Formal integrability; Lie algebra
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:17484
Deposited On:18 Dec 2012 09:34
Last Modified:12 Dec 2018 15:13

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