论文标题
关于谐波孤子的刚性
On the rigidity of harmonic-Ricci solitons
论文作者
论文摘要
在本文中，我们介绍了Harmonic-Ricci孤子的刚性概念，并提供了一些刚性的特征，从而推广了Ricci孤子的一些已知结果。在紧凑型情况下，我们不一定要处理梯度孤子，而在完整的非紧凑型情况下，我们将注意力限制在稳定且萎缩的梯度孤子上。我们表明，刚度可以追溯到某些修改后的曲率张量的消失，这些曲率张紧器考虑到几何形状，其中一个带有光滑地图$φ$的riemannian歧管，称为$φ$ - curvatures，这是对谐波独量的标准曲率的自然概括。
In this paper we introduce the notion of rigidity for harmonic-Ricci solitons and we provide some characterizations of rigidity, generalizing some known results for Ricci solitons. In the compact case we are able to deal with not necessarily gradient solitons while, in the complete non-compact case, we restrict our attention to steady and shrinking gradient solitons. We show that the rigidity can be traced back to the vanishing of certain modified curvature tensors that take into account the geometry a Riemannian manifold equipped with a smooth map $φ$, called $φ$-curvatures, which are a natural generalization of the standard curvature tensors in the setting of harmonic-Ricci solitons.
