{"paper":{"title":"Progress on homogeneous Einstein manifolds and some open probrems","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andreas Arvanitoyeorgos","submitted_at":"2016-05-19T11:04:41Z","abstract_excerpt":"We give an overview of progress on homogeneous Einstein metrics on large classes of homogeneous manifolds, such as generalized flag manifolds and Stiefel manifolds. The main difference between these two classes of homogeneous spaces is that their isotropy representation does not contain/contain equivalent summands. We also discuss a third class of homogeneous spaces that falls into the intersection of such dichotomy, namely the generalized Wallach spaces. We give new invariant Einstein metrics on the Stiefel manifold $V_5\\mathbb{R}^n$ ($n\\ge 7$) and through this example we show how to prove ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05886","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}