Summary
Riemannian manifolds with structure group G 2 are 7-dimensional and have a distinguished 3-form. In this paper such manifolds are treated as analogues of almost Hermitian manifolds. Thus S 7 has structure group G 2 just as S 6 is an almost Hermitian manifold. We study the covariant derivative of the fundamental 3-form as was done in [GH]for almost Hermitian manifolds.
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Fernández, M., Gray, A. Riemannian manifolds with structure groupG 2 . Annali di Matematica pura ed applicata 132, 19–45 (1982). https://doi.org/10.1007/BF01760975
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DOI: https://doi.org/10.1007/BF01760975