Abstract
We study conformal vector fields on space-times which in addition are compatible with the Ricci tensor (so-called conformal Ricci collineations). In the case of Einstein metrics any conformal vector field is automatically a Ricci collineation as well. For Riemannian manifolds, conformal Ricci collineation were called concircular vector fields and studied in the relationship with the geometry of geodesic circles. Here we obtain a partial classification of space-times carrying proper conformal Ricci collineations. There are examples which are not Einstein metrics.
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Kühnel, W., Rademacher, HB. LETTER: Conformal Ricci Collineations of Space-Times. General Relativity and Gravitation 33, 1905–1914 (2001). https://doi.org/10.1023/A:1013091621037
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DOI: https://doi.org/10.1023/A:1013091621037