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Closed G$_2$-structures on non-solvable Lie groups. (arXiv:1712.09664v1 [math.DG])
来源于:arXiv
We investigate the existence of left-invariant closed G$_2$-structures on
seven-dimensional non-solvable Lie groups, providing the first examples of this
type. When the Lie algebra has trivial Levi decomposition, we show that such a
structure exists only when the semisimple part is isomorphic to
$\mathfrak{sl}(2,\mathbb{R})$ and the radical is unimodular and centerless.
Moreover, we classify unimodular Lie algebras with non-trivial Levi
decomposition admitting closed G$_2$-structures. 查看全文>>