{"paper":{"title":"Spectrum of the Laplacian on Quaternionic Kahler Manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Detang Zhou, Peter Li, Shengli Kong","submitted_at":"2007-04-14T03:40:22Z","abstract_excerpt":"Let $M^{4n}$ be a complete quaternionic K\\\"ahler manifold with scalar curvature bounded below by $-16n(n+2)$. We get a sharp estimate for the first eigenvalue $\\lambda_1(M)$ of the Laplacian which is $\\lambda_1(M)\\le (2n+1)^2$. If the equality holds, then either $M$ has only one end, or $M$ is diffeomorphic to $\\mathbb{R}\\times N$ with N given by a compact manifold. Moreover, if $M$ is of bounded curvature, $M$ is covered by the quaterionic hyperbolic space $\\mathbb{QH}^n$ and $N$ is a compact quotient of the generalized Heisenberg group. When $\\lambda_1(M)\\ge \\frac{8(n+2)}3$, we also prove th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.1851","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"}