{
  "abstract": "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 $\\SU(n)^3/Δ\\SO(n)$, obtain a sharp threshold for $\\SU(2n)^3/Δ\\Sp(n)$, and construct asymmetric metrics on three exceptional three-factor families. The four-factor case exhibits a further phenomenon. On \\[ M_9=\\SU(18)^4/Δ\\Sp(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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03593",
  "author_total": 1,
  "authors": [
    {
      "name": "Anna Siffert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/an5c6gw0b2mpq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03593",
  "fulltext_url": null,
  "id": "an5c6gw0b2mpq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03593",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7208704820",
  "pdf_url": "https://arxiv.org/pdf/2609.03593",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/an5c6gw0b2mpq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03593",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03593"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "New Homogeneous Einstein Metrics from Detection",
  "title_text": "New Homogeneous Einstein Metrics from Detection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/an5c6gw0b2mpq",
  "venue": "arXiv",
  "versions": []
}