摘要
This paper extends widely the work in [11]. Existence and non-existence results of isoparametric functions on exotic spheres and Eells-Kuiper projective planes are established. In particular, every homotopy n-sphere (n>. 4) carries an isoparametric function (with certain metric) with 2 points as the focal set, in strong contrast to the classification of cohomogeneity one actions on homotopy spheres [26] (only exotic Kervaire spheres admit cohomogeneity one actions besides the standard spheres). As an application, we improve a beautiful result of Bérard-Bergery [2] (see also pp. 234-235 of [3]).
| 源语言 | 英语 |
|---|---|
| 页（从-至） | 611-629 |
| 页数 | 19 |
| 期刊 | Advances in Mathematics |
| 卷 | 272 |
| DOI | |
| 出版状态 | 已出版 - 6 2月 2015 |
| 已对外发布 | 是 |
指纹
探究 'Isoparametric functions on exotic spheres' 的科研主题。它们共同构成独一无二的指纹。引用此
Qian, C., & Tang, Z. (2015). Isoparametric functions on exotic spheres. Advances in Mathematics, 272, 611-629. https://doi.org/10.1016/j.aim.2014.12.020