Conformal deformations of conic metrics to constant scalar curvature
Conformal deformations of conic metrics to constant scalar curvature
复制标题
圆锥曲线到恒定标量曲率的共形变形
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
J. Rowlett
中科院分区：
文献类型：
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作者：
Thalia D. Jeffres;J. Rowlett
我们考虑一类不完全黎曼度量中的共形变形，它通过允许翘曲和任何紧致流形(不仅仅是球面的商)都是奇异集的“链接”来推广圆锥或分叉奇点。在这类“圆锥度量”中，我们确定了任何符号(正、负或零)的恒定标量曲率的共形变形存在的障碍。对于具有负数量曲率的圆锥度量，我们确定了具有常数量曲率$-1$的二次度量存在共形变形的充分条件；此外，我们证明了该度量在其共形度量类中是唯一的。我们的工作是三维和更高维度的。
We consider conformal deformations within a class of incomplete Riemannian metrics which generalize conic orbifold singularities by allowing both warping and any compact manifold (not just quotients of the sphere) to be the ``link'' of the singular set. Within this class of ``conic metrics,'' we determine obstructions to the existence of conformal deformations to constant scalar curvature of any sign (positive, negative, or zero). For conic metrics with negative scalar curvature, we determine sufficient conditions for the existence of a conformal deformation to a conic metric with constant scalar curvature $-1$; moreover, we show that this metric is unique within its conformal class of conic metrics. Our work is in dimensions three and higher.