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

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Abstract

We investigate the conformally flat semi-Riemannian manifolds withnilpotent Ricci operators. We construct a lot of complete orhomogeneous, conformally flat semi-Riemannian manifolds with nilpotentRicci operators. In this construction, we show interesting relationsbetween the semi-Riemannian geometry and the affine differentialgeometry of centro-affine hypersurfaces.

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Authors and Affiliations

  1. Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo, 112-8610, Japan

    Kyoko Honda

  2. Department of Mathematics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo, 112-8610, Japan

    Kazumi Tsukada

Authors
  1. Kyoko Honda
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  2. Kazumi Tsukada
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Honda, K., Tsukada, K. Conformally Flat Semi-Riemannian Manifolds with Nilpotent Ricci Operators and Affine Differential Geometry. Annals of Global Analysis and Geometry 25, 253–275 (2004). https://doi.org/10.1023/B:AGAG.0000023245.73639.93

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  • DOI: https://doi.org/10.1023/B:AGAG.0000023245.73639.93

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