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arXiv · 1609.01557

Non orientable three-submanifolds of $\mathrm{G}_2-$manifolds

Leonardo Bagaglini
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Abstract

By analogy with associative and co-associative cases we introduce a class of three-dimensional non-orientable submanifolds, of almost $\mathrm{G}_2-$manifolds, modelled on planes lying in a special $\mathrm{G}_2-$orbit. An application of the Cartan-K\"ahler theory shows that some three-manifold can be presented in this way. We also classify all the homogeneous ones in $\mathbb{RP}^7$.

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Leonardo Bagaglini. 2016-09-06. Non orientable three-submanifolds of $\mathrm{G}_2-$manifolds. https://doi.org/10.1515/advgeom-2018-0023

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