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Proof of the radical conjecture for homogeneous Kähler manifolds

Published online by Cambridge University Press:  22 January 2016

Josef Dorfmeister
Josef Dorfmeister*
Affiliation:
Department of Mathematics, University of Kansas Lawrence, Kansas 6604-5, U.S.A.
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In 1967 Gindikin and Vinberg stated the Fundamental Conjecture for homogeneous Kähler manifolds. It (roughly) states that every homogeneous Kähler manifold is a fiber space over a bounded homogeneous domain for which the fibers are a product of a flat with a simply connected compact homogeneous Kähler manifold. This conjecture has been proven in a number of cases (see [6] for a recent survey). In particular, it holds if the homogeneous Kähler manifold admits a reductive or an arbitrary solvable transitive group of automorphisms [5]. It is thus tempting to think about the general case. It is natural to expect that lack of knowledge about the radical of a transitive group G of automorphisms of a homogeneous Kähler manifold M is the main obstruction to a proof of the Fundamental Conjecture for M. Thus it is of importance to consider the Kähler algebra generated by the radical of the Lie algebra of G. Computations in this context suggest that one rather considers Kähler algebras generated by an arbitrary solvable ideal.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 114 , June 1989 , pp. 77 - 122
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

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