Geodesic
Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor
Canadian journal of mathematics, Tome 62 (2010) no. 5, pp. 1037-1057

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DOI

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.
DOI : 10.4153/CJM-2010-059-2
Mots-clés : 53B30, 53C50, Walker metric, Riemann extension, curvature operator, projectively flat and recurrent affine connection 
Calviño-Louzao, E.; García-Río, E.; Vázquez-Lorenzo, R. Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor. Canadian journal of mathematics, Tome 62 (2010) no. 5, pp. 1037-1057. doi: 10.4153/CJM-2010-059-2
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     author = {Calvi\~no-Louzao, E. and Garc{\'\i}a-R{\'\i}o, E. and V\'azquez-Lorenzo, R.},
     title = {Riemann {Extensions} of {Torsion-Free} {Connections} with {Degenerate} {Ricci} {Tensor}},
     journal = {Canadian journal of mathematics},
     pages = {1037--1057},
     year = {2010},
     volume = {62},
     number = {5},
     doi = {10.4153/CJM-2010-059-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-059-2/}
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