{"paper":{"title":"Riemannian geometry on the quantomorphism group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"David G. Ebin, Stephen C. Preston","submitted_at":"2013-02-20T19:06:45Z","abstract_excerpt":"We are interested in the geometry of the group $\\mathcal{D}_q(M)$ of diffeomorphisms preserving a contact form $\\theta$ on a manifold $M$. We define a Riemannian metric on $\\mathcal{D}_q(M)$, compute the corresponding geodesic equation, and show that solutions exist for all time and depend smoothly on initial conditions. In certain special cases (such as on the 3-sphere), the geodesic equation is a simplified version of the quasigeostrophic equation, so we obtain a new geodesic interpretation of this geophysical system. We also show that the genuine quasigeostrophic equation on $S^2$ can be ob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5075","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"}