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 |
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| container_title | Nonlinear analysis |
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| creator | Feitosa, F.E.S. Freitas Filho, A.A. Gomes, J.N.V. |
| description | 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. |
| doi_str_mv | 10.1016/j.na.2017.05.013 |
| format | Article |
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| language | eng |
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| subjects | Curvature Mathematical analysis Nonlinear equations Obstructions Ricci soliton Rigidity results Scalar curvature Warped product |
| title | On the construction of gradient Ricci soliton warped product |
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