Simply transitive groups and Kähler structures on homogeneous Siegel domains
Simply transitive groups and Kähler structures on homogeneous Siegel domains
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同质西格尔域上的简单传递群和凯勒结构
DOI：
10.1090/s0002-9947-1985-0773062-6
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发表时间：
1985
影响因子：
1.3
通讯作者：
J. Dorfmeister
中科院分区：
文献类型：
--
作者：
J. Dorfmeister
． 我们确定了齐次Siegel域D上所有自同构的简传递群作为标准正规j-代数的修正的李代数。证明了D的所有自同构的李代数是一个“标准位置上的完全等距代数”。这意味着D携带一个非正截面曲率的黎曼度规g，满足Lie Iso(D, g) = Lie Aut D。我们确定了D上所有全纯等距群Aut（£>,/）传递作用的Kahler度规f。我们证明了在这种情况下，Aut（D, f）包含一个简单传递分裂可解的子群。利用本文的结果证明了齐次Kahler流形存在可解传递自同构群的基本猜想。
. We determine the Lie algebras of all simply transitive groups of automorphisms of a homogeneous Siegel domain D as modifications of standard normal j-algebras. We show that the Lie algebra of all automorphisms of D is a "complete isometry algebra in standard position". This implies that D carries a riemannian metric g with nonpositive sectional curvature satisfying Lie Iso(D, g) = Lie Aut D. We determine all Kahler metrics f on D for which the group Aut(£>, /) of holomorphic isometries acts transitively. We prove that in this case Aut(D, f) contains a simply transitive split solvable subgroup. The results of this paper are used to prove the fundamental conjecture for homogeneous Kahler manifolds admitting a solvable transitive group of automorphisms.