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Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor
  Published:2010-07-06
 Printed: Oct 2010
Canadian Journal of Mathematics
  • E. Calviño-Louzao,
    Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain
  • E. García-Río,
    Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain
  • R. Vázquez-Lorenzo,
    Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain
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Abstract

{Correspondence} between torsion-free connections with {nilpotent skew-symmetric curvature operator} and IP Riemann extensions is shown. Some consequences are derived in the study of four-dimensional IP metrics and locally homogeneous affine surfaces.
Keywords: Walker metric, Riemann extension, curvature operator, projectively flat and recurrent affine connection Walker metric, Riemann extension, curvature operator, projectively flat and recurrent affine connection
MSC Classifications: 53B30, 53C50 show english descriptions Lorentz metrics, indefinite metrics
Lorentz manifolds, manifolds with indefinite metrics 53B30 - Lorentz metrics, indefinite metrics
53C50 - Lorentz manifolds, manifolds with indefinite metrics
 
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