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December 2019 Calabi–Yau structures and special Lagrangian submanifolds of complexified symmetric spaces
Naoyuki Koike
Illinois J. Math. 63(4): 575-600 (December 2019). DOI: 10.1215/00192082-8018607

Abstract

It is known that there exist Calabi–Yau structures on the complexifications of symmetric spaces of compact type. In this paper, we first construct explicit complete Ricci-flat Kaehler metrics (which give Calabi–Yau structures) for complexified symmetric spaces of arbitrary rank in terms of the Schwarz’s theorem. We consider the case where the Calabi–Yau structure arises from the generalized Stenzel metric. In the complexified symmetric spaces equipped with such a Calabi–Yau structure, we give constructions of special Lagrangian submanifolds of any given phase which are invariant under the actions of symmetric subgroups of the isometry group of the original symmetric space of compact type.

Citation

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Naoyuki Koike. "Calabi–Yau structures and special Lagrangian submanifolds of complexified symmetric spaces." Illinois J. Math. 63 (4) 575 - 600, December 2019. https://doi.org/10.1215/00192082-8018607

Information

Received: 5 February 2019; Revised: 9 September 2019; Published: December 2019
First available in Project Euclid: 19 November 2019

zbMATH: 07136347
MathSciNet: MR4032815
Digital Object Identifier: 10.1215/00192082-8018607

Subjects:
Primary: 53D12
Secondary: 53C35

Rights: Copyright © 2019 University of Illinois at Urbana-Champaign

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Vol.63 • No. 4 • December 2019
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