{"paper":{"title":"Contact action functional, calculus of variation and canonical generating function of Legendrian submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Seungook Yu, Yong-Geun Oh","submitted_at":"2023-11-30T12:39:51Z","abstract_excerpt":"In the present paper, we formulate a contact analogue on the one-jet bundle $J^1B$ of Weinstein's observation which reads the classical action functional on the cotangent bundle is a generating function of any Hamiltonian isotope of the zero section. We do this by identifying the correct action functional which is defined on the space of Hamiltonian-translated (piecewise smooth) horizontal curves of the contact distribution, which we call the Carnot path space. Then we give a canonical construction of the Legendrian generating function which is the Legendrian counterpart of Laudenbach-Sikorav'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.18510","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.18510/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}