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1 November 2001 Calibrated fibrations on noncompact manifolds via group actions
Edward Goldstein
Duke Math. J. 110(2): 309-343 (1 November 2001). DOI: 10.1215/S0012-7094-01-11025-9

Abstract

In this paper we use Lie group actions on noncompact Riemannian manifolds with calibrations to construct calibrated submanifolds. In particular, if we have an $(n-1)$-torus acting on a noncompact Calabi-Yau $n$-fold with a trivial first cohomology, then we have a special Lagrangian fibration on that $n$-fold. We produce several families of examples for this construction and give some applications to special Lagrangian geometry on compact almost Calabi-Yau manifolds. We also use group actions on noncompact $G_2$-manifolds to construct coassociative submanifolds, and we exhibit some new examples of coassociative submanifolds via this setup.

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Edward Goldstein. "Calibrated fibrations on noncompact manifolds via group actions." Duke Math. J. 110 (2) 309 - 343, 1 November 2001. https://doi.org/10.1215/S0012-7094-01-11025-9

Information

Published: 1 November 2001
First available in Project Euclid: 18 June 2004

zbMATH: 1021.53030
MathSciNet: MR1865243
Digital Object Identifier: 10.1215/S0012-7094-01-11025-9

Subjects:
Primary: 53C38
Secondary: 32Q25

Rights: Copyright © 2001 Duke University Press

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Vol.110 • No. 2 • 1 November 2001
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