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Non orientable three-submanifolds of $mathrm{G}_2-$manifolds | | Leonardo Bagaglini
; | | Date: |
6 Sep 2016 | | Abstract: | By analogy with associative and co-associative cases we introduce a class of
three and four-dimensional submanifolds of almost $mathrm{G}_2-$manifolds
(possibly with torsion) modelled on planes lying in a special
$mathrm{G}_2-$orbit. Since $mathrm{G}_2$ reverses such planes there are no
preferred orientations and these manifolds may be non-orientable. Indeed this
happens: using Cartan-K"ahler theory, as done by Bryant in the co-associative
case, we prove that every non orientable, analytic, closed, three-manifold can
be presented in this way. | | Source: | arXiv, 1609.1557 | | Services: | Forum | Review | PDF | Favorites | |
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