Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.04605 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We compute the $\barν$-invariant of homogeneous nearly-parallel $G_2$-structures on Aloff--Wallach spaces $N_{k,l} = SU(3)/S^1_{k,l}$. Using Goette's formulas for the $η$-invariants of homogeneous spaces, we derive an explicit expression for $\barν$ in terms of representation-theoretic data and show that for the two homogeneous nearly-parallel structures $φ^\pm$ on $N_{k,l}$ one has \[\barν(φ^\pm) = \mp 41.\] Additionally, we compare the $\barν$-invariants of the nearly-parallel $G_2$-structures arising from the 3-Sasakian structure.