Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0587.53049
Dorfmeister, Josef
Homogeneous Kähler manifolds admitting a transitive solvable group of automorphisms. (English)
[J] Ann. Sci. Éc. Norm. Supér. (4) 18, 143-180 (1985). ISSN 0012-9593

In this paper the author proves that the "fundamental conjecture" due to {\it E. B. Vinberg} and {\it S. G. Gindikin} [Math. USSR, Sb. 3, 333-351 (1969); translation from Mat. Sb., Nov. Ser. 74(116), 357-377 (1967; Zbl 0153.399)] holds in the case of homogeneous Kähler manifolds admitting a transitive solvable group of automorphisms: A manifold M with this property admits a holomorphic fibering the base of which is analytically isomorphic with a bounded homogeneous domain and each fiber is, with the induced Kähler structure, a locally flat Kähler manifold and it is homogeneous relative to the subgroup of Aut M leaving the fiber invariant. \par For the proof the author generalizes a proof of {\it S. G. Gindikin}, {\it I. I. Pjatetskii-Shapiro} and {\it E. B. Vinberg} [Homogeneous Kähler manifolds, C.I.M.E. $3\sp 0$ Ciclo 1967, Geom. homogen. bounded domains, 1-87 (1968; Zbl 0183.354)] (which worked with split solvable groups). Here the author's main tool is a "modification" of a solvable Kähler algebra to a semidirect product of an Abelian Kähler ideal and a normal j-algebra.
[B.N.Apanasov]

MSC 2000:: *53C30 Homogeneous manifolds
53C55 Complex differential geometry (global)
32M10 Homogeneous complex manifolds
32M05 Automorphism groups of complex spaces

Keywords: homogeneous Kähler manifolds; transitive solvable group of automorphisms; holomorphic fibering; bounded homogeneous domain

Citations: Zbl 0172.378; Zbl 0153.399; Zbl 0183.354

Cited in: Zbl 0596.53055

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]