Osaka Journal of Mathematics

Calibrated submanifolds and reductions of $G_{2}$-manifolds

Kotaro Kawai

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(Co)associative submanifolds in a $G_{2}$-manifold with a free $S^{1}$ or $T^{2}$ action are characterized by submanifolds in the quotient space. Using our method, we construct various examples of (co)associative submanifolds and fibrations on $G_{2}$-manifolds with the $T^{2}$-symmetry such as the cone of the Iwasawa manifold.

Article information

Osaka J. Math., Volume 52, Number 1 (2015), 93-117.

First available in Project Euclid: 24 March 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C38: Calibrations and calibrated geometries 53B25: Local submanifolds [See also 53C40]


Kawai, Kotaro. Calibrated submanifolds and reductions of $G_{2}$-manifolds. Osaka J. Math. 52 (2015), no. 1, 93--117.

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