On G2-manifolds and geometry in dimensions 6 and 8

Key Points

• Geometry on local orbit spaces of $G_2$-manifolds is characterized, highlighting implications for higher dimensions.
• Harmonic morphisms with one-dimensional fibers from $G_2$-manifolds to Einstein manifolds are classified thoroughly.
• Use of Killing vector fields sheds light on the distinct geometrical structure of $G_2$-manifolds.
• Research finds relevance in understanding the deeper connections between $G_2$ and Einstein manifolds through harmonic morphisms.