In this paper we prove that any complete locally conformally flat quasi-Einstein manifold of dimension ≧ 3 is locally a warped product with (n - 1)–dimensional fibers of constant curvature. This result includes also the case of locally conformally flat gradient Ricci solitons.
Locally Conformally Flat Quasi-Einstein Manifolds
Rimoldi, Michele;Mazzieri, Lorenzo;Mantegazza, Carlo;Catino, Giovanni
2010
Abstract
In this paper we prove that any complete locally conformally flat quasi-Einstein manifold of dimension ≧ 3 is locally a warped product with (n - 1)–dimensional fibers of constant curvature. This result includes also the case of locally conformally flat gradient Ricci solitons.File in questo prodotto:
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