Conformally Flat Semi-Riemannian Manifolds with Nilpotent Ricci Operators and Affine Differential Geometry

We investigate the conformally flat semi-Riemannian manifolds with nilpotent Ricci operators. We construct a lot of complete or homogeneous, conformally flat semi-Riemannian manifolds with nilpotent Ricci operators. In this construction, we show interesting relations between the semi-Riemannian geom...

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Bibliographic Details
Published in:Annals of global analysis and geometry 2004-05, Vol.25 (3), p.253-275
Main Authors: Honda, Kyoko, Tsukada, Kazumi
Format: Article
Language:English
Subjects:
Eigenvalues
Geometry
Lie groups
Light
Mathematical analysis
Mathematical models
Studies
Theorems
Topological manifolds
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Summary:We investigate the conformally flat semi-Riemannian manifolds with nilpotent Ricci operators. We construct a lot of complete or homogeneous, conformally flat semi-Riemannian manifolds with nilpotent Ricci operators. In this construction, we show interesting relations between the semi-Riemannian geometry and the affine differential geometry of centro-affine hypersurfaces. [PUBLICATION ABSTRACT]
ISSN:0232-704X
1572-9060
DOI:10.1023/B:AGAG.0000023245.73639.93