## Osaka Journal of Mathematics

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

Kotaro Kawai

#### Abstract

(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

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

Dates
First available in Project Euclid: 24 March 2015

https://projecteuclid.org/euclid.ojm/1427202874

Mathematical Reviews number (MathSciNet)
MR3326604

Zentralblatt MATH identifier
1328.53065

#### Citation

Kawai, Kotaro. Calibrated submanifolds and reductions of $G_{2}$-manifolds. Osaka J. Math. 52 (2015), no. 1, 93--117. https://projecteuclid.org/euclid.ojm/1427202874

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