New Homogeneous Einstein Metrics from Detection

@misc{siffert2026homogeneous,
  title = {{New Homogeneous Einstein Metrics from Detection}},
  author = {Anna Siffert},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03593},
  eprint = {2609.03593},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03593},
}

TY  - UNPB
TI  - New Homogeneous Einstein Metrics from Detection
AU  - Anna Siffert
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03593
UR  - https://arxiv.org/abs/2609.03593
AB  - We use a detection method for invariant Einstein equations to construct and distinguish asymmetric homogeneous Einstein metrics on several families of compact homogeneous spaces. The method retains a geometrically meaningful symmetry-breaking parameter, eliminates the remaining Einstein equations, and then reconstructs positive metrics from the resulting detector. We prove a sharp threshold in a two-factor symplectic family, construct two asymmetric Einstein metrics on each admissible space SU(n)^3/ΔSO(n), obtain a sharp threshold for SU(2n)^3/ΔSp(n), and construct asymmetric metrics on three exceptional three-factor families. The four-factor case exhibits a further phenomenon. On M_9=SU(18)^4/ΔSp(9) the two symmetry types 3+1 and 2+2 are both realized: up to homothety and internal block permutations, the corresponding fixed families contain exactly three asymmetric Einstein metrics, two with three equal horizontal scales and one distinct scale (type 3+1), and one with two equal pairs of horizontal scales (type 2+2). They are pairwise non-isometric, Riemannian irreducible, and not naturally reductive. The 2+2 metric is globally unique in the full positive 2+2 fixed family up to block interchange.
ER  -