Holomorphic invariant forms of a bounded domain
文献类型：期刊论文
| 作者 | Lu QiKeng |
| 刊名 | SCIENCE IN CHINA SERIES A-MATHEMATICS
 |
| 出版日期 | 2008-11-01 |
| 卷号 | 51期号:11页码:1945-1964 |
| 关键词 | complete ortho-normal system holomorphic invariant forms |
| ISSN号 | 1006-9283 |
| DOI | 10.1007/s11425-008-0129-5 |
| 英文摘要 | Given a complete ortho-normal system phi = (phi(0), phi(1), phi(2),...) of L(2)H(D), the space of holomorphic and absolutely square integrable functions in the bounded domain D of C(n), we construct a holomorphic imbedding iota(phi) : D -> F(n, infinity), the complex infinite dimensional Grassmann manifold of rank n. It is known that in F(n, infinity) there are n closed (mu, mu)-forms tau(mu) (mu = 1,..., n) which are invariant under the holomorphic isometric automorphism of F(n, infinity) and generate algebraically all the harmonic differential forms of F(n, infinity). So we obtain in D a set of (mu, mu)- forms iota(phi)*tau(mu) (mu = 1,..., n), which are independent of the system. chosen and are invariant under the bi-holomorphic transformations of D. Especially the differential metric ds(1)(2) associated to the Kahler form iota(phi)*tau(1) is a Kahler metric which differs from the Bergman metric ds(2) of D in general, but in case that the Bergman metric is an Einstein metric, ds(1)(2) differs from ds(2) only by a positive constant factor. |
| 语种 | 英语 |
| WOS记录号 | WOS:000259820400001 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/5585]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Lu QiKeng |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Lu QiKeng. Holomorphic invariant forms of a bounded domain[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS,2008,51(11):1945-1964. |
| APA | Lu QiKeng.(2008).Holomorphic invariant forms of a bounded domain.SCIENCE IN CHINA SERIES A-MATHEMATICS,51(11),1945-1964. |
| MLA | Lu QiKeng."Holomorphic invariant forms of a bounded domain".SCIENCE IN CHINA SERIES A-MATHEMATICS 51.11(2008):1945-1964. |
入库方式： OAI收割
来源：数学与系统科学研究院
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