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June 2003 Conformally Flat Semi-Riemannian Manifolds with Commuting Curvature and Ricci Operators
Kyoko HONDA
Tokyo J. Math. 26(1): 241-260 (June 2003). DOI: 10.3836/tjm/1244208691

Abstract

We classify the conformally flat, semi-Riemannian manifolds satisfying $R(X,Y) \cdot Q = 0$, where $R$ and $Q$ are the curvature tensor and the Ricci operator, respectively. As the cases which do not occur in the Riemannian manifolds, the Ricci operator $Q$ has pure imaginary eigenvalues or it satisfies $Q^2 = 0$.

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Kyoko HONDA. "Conformally Flat Semi-Riemannian Manifolds with Commuting Curvature and Ricci Operators." Tokyo J. Math. 26 (1) 241 - 260, June 2003. https://doi.org/10.3836/tjm/1244208691

Information

Published: June 2003
First available in Project Euclid: 5 June 2009

zbMATH: 1055.53054
MathSciNet: MR1982008
Digital Object Identifier: 10.3836/tjm/1244208691

Subjects:
Primary: 53C50
Secondary: 53A30

Rights: Copyright © 2003 Publication Committee for the Tokyo Journal of Mathematics

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Vol.26 • No. 1 • June 2003
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