Rigidity of invariant complex structures

Dotti Miatello, Isabel

doi:10.1090/S0002-9947-1993-1100696-6

Rigidity of invariant complex structures
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Trans. Amer. Math. Soc. 338 (1993), 159-172 Request permission

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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