{"paper":{"title":"On adding a variable to a Frobenius manifold and generalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"math.DG","authors_text":"Liana David","submitted_at":"2012-01-04T17:56:39Z","abstract_excerpt":"Let \\pi : V \\rightarrow M be a (real or holomorphic) vector bundle whose base has an almost Frobenius structure (\\circ_{M},e_{M}, g_{M}) and typical fiber has the structure of a Frobenius algebra (\\circ_{V},e_{V},g_{V}). Using a connection D on the bundle V and a morphism \\alpha : V \\rightarrow TM, we construct an almost Frobenius structure (\\circ,e_{V},g) on the manifold V and we study when it is Frobenius. We describe all (real) positive-definite Frobenius structures on V, obtained in this way, when M is a semisimple Frobenius manifold with non-vanishing rotation coefficients. In the holomor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0948","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"}