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We prove that a primitive immersion from the two-sphere into the full flag manifold which has constant curvature with respect to\n                    <jats:italic>at least one<\/jats:italic>\n                    invariant metric is unitarily equivalent to the primitive lift of a Veronese map, hence it has constant curvature with respect to\n                    <jats:italic>all<\/jats:italic>\n                    invariant metrics. We prove a partial generalization of this result to the case where the domain is a general simply connected Riemann surface. On the way, we consider the problem of finding the invariant metric on the flag manifold, under a certain normalization condition, that maximizes the induced area of the two-sphere by a given primitive immersion.\n                  <\/jats:p>","DOI":"10.1007\/s00025-026-02598-4","type":"journal-article","created":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T12:00:31Z","timestamp":1770379231000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Primitive Immersions of Constant Curvature of Surfaces into Flag Manifolds"],"prefix":"10.1007","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9578-2380","authenticated-orcid":false,"given":"Rui","family":"Pacheco","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6886-2545","authenticated-orcid":false,"given":"Mehmood Ur","family":"Rehman","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,2,6]]},"reference":[{"issue":"4","key":"2598_CR1","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1007\/s00605-021-01516-w","volume":"194","author":"A Aleman","year":"2021","unstructured":"Aleman, A., Pacheco, R., Wood, J.C.: Harmonic maps and shift-invariant subspaces. 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