{"paper":{"title":"Teichm\\\"uller Space Is Totally Geodesic In Goldman Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Qiongling Li","submitted_at":"2013-01-08T08:35:33Z","abstract_excerpt":"We construct a new Riemannian metric on Goldman space $\\mathcal{B}(S)$, the space of the equivalence classes of convex projective structures on the surface $S$, and then prove the new metric, as well as the metric of Darvishzadeh and Goldman, restricts to be the Weil-Petersson metric on Teichm$\\ddot{u}$ller space, embedded as a submanifold of Goldman space $\\mathcal{B}(S)$. Moreover, Teichm$\\ddot{u}$ller space endowed with the Weil-Petersson metric then is totally geodesic in the Riemannian manifold $\\mathcal{B}(S)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1442","kind":"arxiv","version":2},"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"}