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Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor

Published online by Cambridge University Press:  20 November 2018

E. Calviño-Louzao ,
E. García-Río  and
R. Vázquez-Lorenzo
E. Calviño-Louzao*
Affiliation:
Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain
E. García-Río*
Affiliation:
Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain
R. Vázquez-Lorenzo*
Affiliation:
Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain
*
estebcl@edu.xunta.es
eduardo.garcia.rio@usc.es
ravazlor@edu.xunta.es
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Abstract

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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

53B3053C50Walker metricRiemann extensioncurvature operatorprojectively flat and recurrent affine connection
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 5 , 01 October 2010 , pp. 1037 - 1057
Copyright
Copyright © Canadian Mathematical Society 2010

Footnotes

Supported by projects MTM2006-01432 and PGIDIT06PXIB207054PR (Spain).

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