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Keywords:
cocalibrated $G_2$-manifolds; connections with torsion
cocalibrated $G_2$-manifolds; connections with torsion
Summary:
Any 7-dimensional cocalibrated $G_2$-manifold admits a unique connection $\nabla$ with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the $\nabla$-Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of $\nabla$-parallel vector fields.
References:
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