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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rigidity of invariant complex structures


Author: Isabel Dotti Miatello
Journal: Trans. Amer. Math. Soc. 338 (1993), 159-172
MSC: Primary 32M10; Secondary 32C17, 53C55
MathSciNet review: 1100696
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Abstract: A Kähler solvmanifold is a connected Kähler manifold $ (M,j,\left\langle , \right\rangle )$ admitting a transitive solvable group of automorphisms. In this paper we study the isomorphism classes of Kähler structures $ (j,\left\langle , \right\rangle )$ turning $ M$ into a Kähler solvmanifold. In the case when $ (M,j,\left\langle , \right\rangle )$ is irreducible and simply connected we show that any Kähler structure on $ M$, having the same group of automorphisms, is isomorphic to $ (j,\left\langle , \right\rangle )$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1100696-6
PII: S 0002-9947(1993)1100696-6
Article copyright: © Copyright 1993 American Mathematical Society