闭三维流形上的共轭线性化 Ricci 流
微分几何
2009-07-14 v4 数学物理
math.MP
摘要
我们刻画了闭有界几何三维流形上的共轭线性化 Ricci 流及其关联的反向热核。我们讨论了它们的性质，并引入了 Ricci 流共轭约束集的概念，该概念刻画了一种对 Ricci 流平均度量依赖几何数据的方式。我们还给出了 Ricci 流度量本身及其 Ricci 张量关于共轭线性化 Ricci 流热核的积分表示。这些结果可自然推广到闭 n 维流形，对 Ricci 流及其线性化给出了各种守恒律、单调性公式和渐近公式。
引用
@article{arxiv.0710.3342,
title = {The Conjugate Linearized Ricci Flow on Closed 3-Manifolds},
author = {Mauro Carfora},
journal= {arXiv preprint arXiv:0710.3342},
year = {2009}
}
备注
We added a few references and indications of which result extends to n-dimensional manifold. A few complex computations have been presented in full detail. This version of the paper matches the work to appear in Annali della Scuola Normale Superiore di Pisa