Holomorphic invariant forms of a bounded domain

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	Holomorphic invariant forms of a bounded domain
	LU QiKeng
	2008
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.