{"paper":{"title":"The Einstein-Hilbert action of the space of holomorphic maps from S^2 to CP^k","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"L.S. Alqahtani","submitted_at":"2013-03-08T15:58:08Z","abstract_excerpt":"Let $\\mathcal{H}_{n,k}(\\Sigma)$ be the space of degree $n\\geq 1$ holomorphic maps from a compact Riemann surface $\\Sigma $ to $\\mathbb{C}P^k$. In the case $\\Sigma=S^2$ and $n=1$, the $L^2$ metric on $\\mathcal{H}_{1,k}(S^2)$ was computed exactly by Speight. In this paper, the Ricci curvature tensor and the scalar curvature on $\\mathcal{H}_{1,k}(S^2)$ are determined explicitly for $k\\geq 2$. An exact direct computation of the Einstein-Hilbert action with respect to the $L^2$ metric on $\\mathcal{H}_{1,k}(S^2)$ is made and shown to coincide with a formula conjectured by Baptista."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2036","kind":"arxiv","version":3},"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"}