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The central object describing these properties is the quantum geometric tensor, which unifies the Berry curvature and the quantum metric. In this work, we use the differential-geometric framework of vector bundles to analyze the properties of parameter-dependent quantum states and generalize the quantum geometric tensor to this setting. This construction is based on a general connection on a Hermitian vector bundle, which defines a notion of quantum state transport in parameter space, and a sub-bundle projector, which constrains the set of accessible quantum states. We show that the sub-bundle geometry is similar to that of submanifolds in Riemannian geometry and is described by generalized Gauss-Codazzi-Mainardi equations. This leads to a novel definition of the quantum geometric tensor that contains an additional curvature contribution. To illustrate our results, we describe the sub-bundle geometry arising in the semiclassical treatment of Dirac fields propagating in curved spacetime and show how the quantum geometric tensor, with its additional curvature contributions, is obtained in this case. As a concrete example, we consider Dirac fermions confined to a hyperbolic plane and demonstrate how spatial curvature influences the quantum geometry. This work sets the stage for further exploration of quantum systems in curved geometries, with applications in both high-energy physics and condensed matter systems.<\/jats:p>","DOI":"10.22331\/q-2026-01-14-1965","type":"journal-article","created":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T16:32:08Z","timestamp":1768408328000},"page":"1965","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Quantum geometric tensors from sub-bundle geometry"],"prefix":"10.22331","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1242-4041","authenticated-orcid":false,"given":"Marius A.","family":"Oancea","sequence":"first","affiliation":[{"name":"University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6905-0183","authenticated-orcid":false,"given":"Thomas B.","family":"Mieling","sequence":"additional","affiliation":[{"name":"University of Vienna, Faculty of Physics and Research Network TURIS, Boltzmanngasse 5, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1303-1247","authenticated-orcid":false,"given":"Giandomenico","family":"Palumbo","sequence":"additional","affiliation":[{"name":"School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"M. 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