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arXiv · 1506.00342

On the construction of gradient Ricci soliton warped product

F. E. S. Feitosa·A. A. Freitas Filho·J. N. V. Gomes
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Abstract

In this paper we show that an expanding or steady gradient Ricci soliton warped product $B^n\times_f F^m$, $m>1$, 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.

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F. E. S. Feitosa, A. A. Freitas Filho, J. N. V. Gomes. 2015-06-01. On the construction of gradient Ricci soliton warped product. https://doi.org/10.1016/j.na.2017.05.013

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