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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On hyper Kähler manifolds associated to Lagrangian Kähler submanifolds of $T^\ast \mathbb \{C\}^n$
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by Vicente Cortés PDF
Trans. Amer. Math. Soc. 350 (1998), 3193-3205 Request permission


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:
  • 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.
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 3193-3205
  • MSC (1991): Primary 53C25
  • DOI:
  • MathSciNet review: 1466946