Illinois Journal of Mathematics

Calabi–Yau structures and special Lagrangian submanifolds of complexified symmetric spaces

Naoyuki Koike

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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.

Article information

Source
Illinois J. Math., Volume 63, Number 4 (2019), 575-600.

Dates
Received: 5 February 2019
Revised: 9 September 2019
First available in Project Euclid: 19 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1574154084

Digital Object Identifier
doi:10.1215/00192082-8018607

Mathematical Reviews number (MathSciNet)
MR4032815

Zentralblatt MATH identifier
07136347

Subjects
Primary: 53D12: Lagrangian submanifolds; Maslov index
Secondary: 53C35: Symmetric spaces [See also 32M15, 57T15]

Citation

Koike, Naoyuki. Calabi–Yau structures and special Lagrangian submanifolds of complexified symmetric spaces. Illinois J. Math. 63 (2019), no. 4, 575--600. doi:10.1215/00192082-8018607. https://projecteuclid.org/euclid.ijm/1574154084


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