KMS Of Academy of mathematics and systems sciences, CAS
Holomorphic invariant forms of a bounded domain | |
LU QiKeng | |
2008-01-01 | |
发表期刊 | Science in China. Series A: Mathematics |
ISSN | 1006-9283 |
卷号 | 51期号:11页码:1945 |
摘要 | Given a complete ortho-normal system ψ= (ψ_0,ψ_1,ψ_2…) of L~2H(D),the space of holomorphic and absolutely square integrable functions in the bounded domain D of C~n,we construct a holomorphic imbedding l_ψ:D→ζ(n,∞),the complex infinite dimensional Grassmann manifold of rank n.It is known that in ζ(n,∞) there are n closed (μ,μ)-forms Tμ (μ=1,...,n) which are invariant under the holomorphic isometric automorphism of ζ(n,∞) and generate algebraically all the harmonic differential forms of ζ(n,∞).So we obtain in D a set of (μ,μ)-forms l_ψ~*T_μ (μ=1,...,n),which are independent of the system ψ chosen and are invariant under the bi-holomorphic transformations of D.Especially the differential metric ds_1~2 associated to the Kahler form l_ψ~*T_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 |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/5586 |
专题 | 中国科学院数学与系统科学研究院 |
作者单位 | Institute of Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences |
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. |
APA | LU QiKeng.(2008).Holomorphic invariant forms of a bounded domain.Science in China. Series A: Mathematics,51(11),1945. |
MLA | LU QiKeng."Holomorphic invariant forms of a bounded domain".Science in China. Series A: Mathematics 51.11(2008):1945. |
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