Tokyo Journal of Mathematics

Conformally Flat Semi-Riemannian Manifolds with Commuting Curvature and Ricci Operators

Kyoko HONDA

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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 $Q^2 = 0$.

Article information

Source
Tokyo J. Math., Volume 26, Number 1 (2003), 241-260.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208691

Digital Object Identifier
doi:10.3836/tjm/1244208691

Mathematical Reviews number (MathSciNet)
MR1982008

Zentralblatt MATH identifier
1055.53054

Subjects
Primary: 53C50: Lorentz manifolds, manifolds with indefinite metrics
Secondary: 53A30: Conformal differential geometry

Citation

HONDA, Kyoko. Conformally Flat Semi-Riemannian Manifolds with Commuting Curvature and Ricci Operators. Tokyo J. Math. 26 (2003), no. 1, 241--260. doi:10.3836/tjm/1244208691. https://projecteuclid.org/euclid.tjm/1244208691


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