The goal of this paper is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these nonexistence results generalize to a broader context certain estimates and rigidity obtained when studying warped product Einstein manifolds. When the soliton is shrinking, it is presented as a nonexistence theorem with no counterpart in the Einstein case, which is proved using properties of the first eigenvalue of a weighted Laplacian.

中文翻译：

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关于非紧扭曲积 Ricci 孤子

本文的目标是研究完全非紧扭曲积梯度 Ricci 孤子。不存在的结果、扭曲函数及其梯度的估计都得到了证明。当孤子稳定或扩展时，这些不存在的结果可以推广到更广泛的背景，即在研究扭曲乘积爱因斯坦流形时获得的某些估计和刚性。当孤子收缩时，它表现为一个不存在定理，在爱因斯坦情况下没有对应物，这是使用加权拉普拉斯算子的第一特征值的性质证明的。