Constant scalar curvature metrics on Hirzebruch surfaces
Constant scalar curvature metrics on Hirzebruch surfaces
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Hirzebruch 曲面上的恒定标量曲率度量
DOI：
10.1007/s10455-014-9419-z
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发表时间：
2014
影响因子：
0.7
通讯作者：
Nobuhiko Otoba
中科院分区：
文献类型：
--
作者：
Nobuhiko Otoba;Jimmy Petean;Nobuhiko Otoba
我们在每个Hirzebruch曲面上构造了具有常数量曲率的光滑黎曼度量。这些度量考虑了这些流形上的复杂结构、纤维束结构和同质的李群作用。这种构造被简化为一个称为Duffing方程的常微分方程式。给出了具有较大等距群的Hirzebruch曲面上的Bach平坦度量的颂歌。
We construct smooth Riemannian metrics with constant scalar curvature on each Hirzebruch surface. These metrics respect the complex structures, fiber bundle structures, and Lie group actions of cohomogeneity one on these manifolds. The construction is reduced to an ordinary differential equation called the Duffing equation. An ODE for Bach-flat metrics on Hirzebruch surfaces with large isometry group is also derived.