论文标题
在非扭曲的产品Ricci Solitons上
On noncompact warped product Ricci solitons
论文作者
论文摘要
本文的目的是调查完整的非扭曲产品梯度RICCI Solitons。不存在的结果，证明了翘曲功能及其梯度的估计。当孤子稳定或扩展这些不存在时，在研究扭曲的产物爱因斯坦歧管时获得的更广泛的环境概括了某些PDE估计和刚度。当孤子萎缩时，在爱因斯坦案例中提出了一个不存在的定理，没有同类情况，这是使用加权laplacian的第一个特征值的特性证明的。
The goal of this article 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 pde estimates and rigidity obtained when studying warped product Einstein manifolds. When the soliton is shrinking, it is presented a nonexistence theorem with no counterpart in the Einstein case, which is proved using properties of the first eigenvalue of a weighted Laplacian.
