The intrinsic structure of the Petrov classification

• J. M. Pozo ^[1] ; J. M. Parra ^[1]
  1. [1] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
• Localización: Proceedings of the XXIII Spanish Relativity Meeting on Reference Frames and Gravitomagnetism: Valladolid, Spain, 6-9 September 2000 / coord. por José Fernando Pascual Sánchez, Luis Floría, Angel San Miguel Blanco, F. Vicente, 2001, ISBN 9810246315, págs. 353-358
• Idioma: inglés
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• Resumen

  • We give a new presentation of the Petrov classification of Einstein spaces. In our approach, the space of bivectors A2, which underlies the double 2-form nature of the Riemann tensor, is treated as subspace of the whole Grassmann space A, on which the Clifford geometric algebra is naturally defined. We use this product to make explicit the intrinsic complex structure that bivector space contains, without introducing any imaginary unit i.