Locally conformal parallel $G_2$ and $Spin(7)$ manifolds

Abstract

We characterize compact locally conformal parallel $G_2$ (respectively, $Spin(7)$) manifolds as fiber bundles over $S^1$ with compact nearly Kähler (respectively, compact nearly parallel $G_2$) fiber. A more specific characterization is provided when the local parallel structures are flat.

References updated

References in corpus (1)

• Killing spinor equations in dimension 7 and geometry of integrable G_2-manifolds

Cited by in corpus (4)

• Curvature decomposition of G_2 manifolds
• Einstein locally conformal calibrated $G_2$-structures
• An intrinsic volume functional on almost complex 6-manifolds and nearly Kaehler geometry
• Goto's deformation theory of geometric structures, a Lie-theoretical description