非全同构的完整周期度量与常标量曲率
微分几何
2025-10-07 v1 偏微分方程分析
摘要
我们证明了存在无限多个两两非全同构、完整且具有常标量曲率的度量，这些度量以 （其中 ）上的圆形度量的共形形式出现。这些度量通过将定义在 与紧双曲 流形乘积上的 Yamabe 度量拉回来获得。我们的主要结果证明了这些解在全同构意义上是普遍不同的。我们的论证核心依赖于 Due to Obata 和 Ferrand 的经典刚性定理，这些定理描述了以其共形群为特征的圆球。
引用
@article{arxiv.2510.04351,
title = {Nonhomothetic complete periodic metrics with constant scalar curvature},
author = {João H. Andrade and Jeffrey S. Case and Paolo Piccione and Juncheng Wei},
journal= {arXiv preprint arXiv:2510.04351},
year = {2025}
}
备注
This is a companion paper to arXiv:2310.15798 which discusses only the case of the Yamabe and singular Yamabe problem for constant scalar curvature metrics. We split the papers in two due to the broader interest in scalar curvature; this paper also includes a more detailed discussion of nonuniqueness. 13 pages