Splitting submanifolds in rational homogeneous spaces of Picard number one
文献类型：期刊论文
| 作者 | Ding, Cong1,2 |
| 刊名 | MATHEMATISCHE ZEITSCHRIFT
 |
| 出版日期 | 2022-01-15 |
| 页码 | 25 |
| 关键词 | Splitting tangent sequence Compact Hermitian symmetric space Rational homogeneous space Holomorphic vector field |
| ISSN号 | 0025-5874 |
| DOI | 10.1007/s00209-022-02967-z |
| 英文摘要 | Let M be a complex manifold. We prove that a compact submanifold S subset of M with splitting tangent sequence (called a splitting submanifold) is rational homogeneous when M is in a large class of rational homogeneous spaces of Picard number one. Moreover, when M is irreducible Hermitian symmetric, we prove that S must be also Hermitian symmetric. These cover some of the results given in Jahnke (Math Z 251(3):491-507, https://doi.org/10.1007/s00209-005-0817-6, 2005). The basic tool we use is the restriction and projection map pi of the global holomorphic vector fields on the ambient space which is induced from the splitting condition. The usage of global holomorphic vector fields may help us set up a new scheme to classify the splitting submanifolds in explicit examples, as an example we give a differential geometric proof for the classification of compact splitting submanifolds with dim >= 2 in a hyperquadric, which has been proven in Jahnke (2005) using algebraic geometry. |
| 资助项目 | University Postgraduate Fellowship of HKU[E0900501] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000742808400001 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59883]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Ding, Cong |
| 作者单位 | 1.Univ Hong Kong, Dept Math, Pokfulam Rd, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Ding, Cong. Splitting submanifolds in rational homogeneous spaces of Picard number one[J]. MATHEMATISCHE ZEITSCHRIFT,2022:25. |
| APA | Ding, Cong.(2022).Splitting submanifolds in rational homogeneous spaces of Picard number one.MATHEMATISCHE ZEITSCHRIFT,25. |
| MLA | Ding, Cong."Splitting submanifolds in rational homogeneous spaces of Picard number one".MATHEMATISCHE ZEITSCHRIFT (2022):25. |
入库方式： OAI收割
来源：数学与系统科学研究院
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