Splitting submanifolds in rational homogeneous spaces of Picard number one

doi:10.1007/s00209-022-02967-z

CSpace

	Splitting submanifolds in rational homogeneous spaces of Picard number one
	Ding, Cong 1,2
	2022-01-15
发表期刊	MATHEMATISCHE ZEITSCHRIFT
ISSN	0025-5874
页码	25
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.
关键词	Splitting tangent sequence Compact Hermitian symmetric space Rational homogeneous space Holomorphic vector field
DOI	10.1007/s00209-022-02967-z
收录类别	SCI
语种	英语
资助项目	University Postgraduate Fellowship of HKU[E0900501]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000742808400001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59884
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.