CONFORMAL DIFFEOMORPHISMS PRESERVING THE RICCI TENSOR

Authors
KUHNEL W RADEMACHER HB
Citation
W. Kuhnel et Hb. Rademacher, CONFORMAL DIFFEOMORPHISMS PRESERVING THE RICCI TENSOR, Proceedings of the American Mathematical Society, 123(9), 1995, pp. 2841-2848
Citations number
26
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
123
Issue
9
Year of publication
1995
Pages
2841 - 2848
Database
ISI
SICI code
0002-9939(1995)123:9<2841:CDPTRT>2.0.ZU;2-B
Abstract
We characterize semi-Riemannian manifolds admitting a global conformal transformation such that the difference of the two Ricci tensors is a constant multiple of the metric. Unless the conformal transformation is homothetic, the only possibilities are standard Riemannian spaces o f constant sectional curvature and a particular warped product with a Ricci flat Riemannian manifold.