Schoen-Yau-Gromov-Lawson theory and isoparametric foliations
Schoen-Yau-Gromov-Lawson theory and isoparametric foliations
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DOI：
10.4310/cag.2012.v20.n5.a4
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发表时间：
2011-07
期刊：
影响因子：
--
通讯作者：
Zizhou Tang;Y. Xie;Wenjiao Yan
中科院分区：
文献类型：
--
作者：
Zizhou Tang;Y. Xie;Wenjiao Yan
受著名的Schoen-Yau-Gromov-Lawson关于正标量曲率度量的外科理论的启发，我们在单位球面上构造了一个与极小等参超曲面相关的双流形。由此产生的双流形带有正标量曲率的度量和等参叶理。为了研究二重流形的拓扑结构，我们利用K-理论和FKM型Clifford代数的表示，完全确定了齐次情形下奇异轨道的迷向子群。
Motivated by the celebrated Schoen-Yau-Gromov-Lawson surgery theory on metrics of positive scalar curvature, we construct a double manifold associated with a minimal isoparametric hypersurface in the unit sphere. The resulting double manifold carries a metric of positive scalar curvature and an isoparametric foliation as well. To investigate the topology of the double manifolds, we use K-theory and the representation of the Clifford algebra for the FKM-type, and determine completely the isotropy subgroups of singular orbits for homogeneous case.