Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor

Calviño-Louzao, E. ; García-Río, E. ; Vázquez-Lorenzo, R.

Canadian journal of mathematics, Tome 62 (2010) no. 5, pp. 1037-1057

Résumé

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.

Détail

DOI : 10.4153/CJM-2010-059-2

Mots-clés : 53B30, 53C50, Walker metric, Riemann extension, curvature operator, projectively flat and recurrent affine connection

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