Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Simply transitive groups and Kähler structures on homogeneous Siegel domains

Author: Josef Dorfmeister
Journal: Trans. Amer. Math. Soc. 288 (1985), 293-305
MSC: Primary 32M10; Secondary 53C55
MathSciNet review: 773062
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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 $\tilde g$ with nonpositive sectional curvature satisfying Lie $\operatorname {Iso}(D,\tilde g) = \operatorname {Lie}\; \operatorname {Aut} \text {D}$. We determine all Kähler metrics $f$ on $D$ for which the group $\operatorname {Aut}(D,f)$ of holomorphic isometries acts transitively. We prove that in this case $\operatorname {Aut}(D,f)$ contains a simply transitive split solvable subgroup. The results of this paper are used to prove the fundamental conjecture for homogeneous Kähler manifolds admitting a solvable transitive group of automorphisms.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32M10, 53C55

Retrieve articles in all journals with MSC: 32M10, 53C55

Additional Information

Keywords: Homogeneous bounded domain, Kähler metric, solvable transitive group of automorphisms
Article copyright: © Copyright 1985 American Mathematical Society