On the construction of gradient Ricci soliton warped product

In this paper we show that an expanding or steady gradient Ricci soliton warped product Bn×fFm, m>1, whose warping function f reaches both maximum and minimum must be a Riemannian product. Moreover, we present a necessary and sufficient condition for constructing a gradient Ricci soliton warped p...

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Veröffentlicht in:Nonlinear analysis 2017-09, Vol.161, p.30-43
Hauptverfasser: Feitosa, F.E.S., Freitas Filho, A.A., Gomes, J.N.V.
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper we show that an expanding or steady gradient Ricci soliton warped product Bn×fFm, m>1, whose warping function f reaches both maximum and minimum must be a Riemannian product. Moreover, we present a necessary and sufficient condition for constructing a gradient Ricci soliton warped product. As an application, we present a class of expanding Ricci soliton warped product having as a fiber an Einstein manifold with non-positive scalar curvature. We also discuss some obstructions to this construction, especially in the case when the base of the warped product is compact.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2017.05.013