Locally conformal parallel \(G_2\) and \(\operatorname{Spin}(7)\) manifolds
The authors establish characterizations of compact locally conformal parallel \(G_2\), (respectively \(\text{Spin}(7)\)), manifolds as fiber bundles over \(S^1\) with compact-nearly Kähler (respectively compact nearly parallel \(G_2\) ) fiber. These are given by their Theorems A and B, and they also consider the more specific characterization when the local parallel structures are flat. Contents include: Introduction; Preliminaries; Structure of compact manifolds (which contains proofs' of Theorems A and B); and a Bibliography of thirty references.
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