无旋转对称性的Ricci流颈缩
微分几何
2014-10-23 v3
摘要
我们研究Ricci流的“扭曲Berger”解：广义扭曲积，每个纤维上的度量是左不变Berger度量。我们证明该结构在流下保持不变，这些解在有限时间内形成颈缩奇点，并且在精确意义上，它们在奇点集的时空邻域内渐近接近圆乘积度量。这些是第一个没有旋转对称性但在局部发展有限时间奇点时渐近旋转对称的Ricci流解的例子。
引用
@article{arxiv.1312.2933,
title = {Ricci flow neckpinches without rotational symmetry},
author = {James Isenberg and Dan Knopf and Natasa Sesum},
journal= {arXiv preprint arXiv:1312.2933},
year = {2014}
}
备注
We correct a miscalculation of some terms in equation (22) and its subsequent uses. The main results of the paper are unchanged, because the methods employed in the proofs are robust enough to give the needed estimates, with only insignificant changes of constants