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On hyper Kähler manifolds associated to Lagrangian Kähler submanifolds of $T^*\mathbb{C}^n$


Author: Vicente Cortés
Journal: Trans. Amer. Math. Soc. 350 (1998), 3193-3205
MSC (1991): Primary 53C25
DOI: https://doi.org/10.1090/S0002-9947-98-02156-4
MathSciNet review: 1466946
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Abstract: For any Lagrangian Kähler submanifold $M \subset T^*\mathbb{C}^n$, there exists a canonical hyper Kähler metric on $T^*M$. A Kähler potential for this metric is given by the generalized Calabi Ansatz of the theoretical physicists Cecotti, Ferrara and Girardello. This correspondence provides a method for the construction of (pseudo) hyper Kähler manifolds with large automorphism group. Using it, an interesting class of pseudo hyper Kähler manifolds of complex signature $(2,2n)$ is constructed. For any manifold $N$ in this class a group of automorphisms with a codimension one orbit on $N$ is specified. Finally, it is shown that the bundle of intermediate Jacobians over the moduli space of gauged Calabi Yau 3-folds admits a natural pseudo hyper Kähler metric of complex signature $(2,2n)$.


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Additional Information

Vicente Cortés
Affiliation: Mathematisches Institut der Universität Bonn, Beringstr. 1, 53115 Bonn, Germany
Email: vicente@math.uni-bonn.de

DOI: https://doi.org/10.1090/S0002-9947-98-02156-4
Received by editor(s): August 29, 1996
Additional Notes: Supported by the Alexander von Humboldt Foundation and MSRI (Berkeley). Research at MSRI is supported in part by grant DMS-9022140.
Article copyright: © Copyright 1998 American Mathematical Society

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