{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T12:44:50Z","timestamp":1785415490493,"version":"3.56.0"},"reference-count":58,"publisher":"American Physical Society (APS)","issue":"1","license":[{"start":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T00:00:00Z","timestamp":1769731200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2026,1,9]]},"abstract":"<jats:p>An antlike observer confined to a two-dimensional surface traversed by stripes would wonder whether such a striped landscape could be devised in such a way as to appear to be the same wherever they go. Differently stated, this is the problem studied in this paper. In a more technical jargon, we determine all possible  nematic fields on a smooth surface. It was already known that for such a field to exist, the surface must have constant  Gaussian curvature. Here we show that all uniform nematic fields on such a surface are parallel transported (in Levi-Civita's sense) by special systems of geodesics, which are termed . We prove that, for every geodesic on the surface, there are  systems of uniform geodesics that include it; they are conventionally called  and , to evoke handedness. We found explicitly all uniform fields for Beltrami's pseudosphere. Since both geodesics and uniformity are preserved under isometries, by a classical theorem of Minding, the solution for the pseudosphere carries over all other admissible surfaces, thus providing a general solution to the problem (at least in principle). The proved existence of surface nematic uniform fields suggests the definition of a generalized intrinsic elastic energy for fluid membranes with nematic order, which is but one of the many possible applications of our geometric result.<\/jats:p>","DOI":"10.1103\/xpvv-zv23","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T20:12:36Z","timestamp":1767989556000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Surface nematic uniformity"],"prefix":"10.1103","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4605-8059","authenticated-orcid":true,"given":"Andrea","family":"Pedrini","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00s6t1f81","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e0 di Pavia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2295-8055","authenticated-orcid":true,"given":"Epifanio G.","family":"Virga","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00s6t1f81","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e0 di Pavia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,1,30]]},"reference":[{"key":"xpvv-zv23Cc1R1","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(86)90231-1","type":"journal-article"},{"key":"xpvv-zv23Cc2R1","doi-asserted-by":"publisher","DOI":"10.1051\/jphys:019870048070108500","type":"journal-article"},{"key":"xpvv-zv23Cc3R1","doi-asserted-by":"publisher","DOI":"10.1051\/jphys:0198700480120205900","type":"journal-article"},{"key":"xpvv-zv23Cc4R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.67.1169","type":"journal-article"},{"key":"xpvv-zv23Cc5R1","doi-asserted-by":"publisher","DOI":"10.1051\/jp2:1992133","type":"journal-article"},{"key":"xpvv-zv23Cc6R1","doi-asserted-by":"publisher","DOI":"10.1140\/epje\/i2008-10441-1","type":"journal-article"},{"key":"xpvv-zv23Cc7R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.021711","type":"journal-article"},{"key":"xpvv-zv23Cc8R1","doi-asserted-by":"publisher","DOI":"10.1515\/znc-1973-11-1209","type":"journal-article"},{"key":"xpvv-zv23Cc9R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/43\/44\/445207","type":"journal-article"},{"key":"xpvv-zv23Cc10R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/aad1cb","type":"journal-article"},{"key":"xpvv-zv23Cc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.108.207803","type":"journal-article"},{"key":"xpvv-zv23Cc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.90.012501","type":"journal-article"},{"key":"xpvv-zv23Cc13R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.97.052706","type":"journal-article"},{"key":"xpvv-zv23Cc14R1","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2005.54.2613","type":"journal-article"},{"key":"xpvv-zv23Cc15R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.052701","type":"journal-article"},{"key":"xpvv-zv23Cc16R1","doi-asserted-by":"publisher","DOI":"10.1080\/21680396.2019.1581103","type":"journal-article"},{"key":"xpvv-zv23Cc17R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.6.011033","type":"journal-article"},{"key":"xpvv-zv23Cc18R1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-conmatphys-031620-105712","type":"journal-article"},{"key":"xpvv-zv23Cc19R1","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-022-09833-6","type":"journal-article"},{"key":"xpvv-zv23Cc20R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.012703","type":"journal-article"},{"key":"xpvv-zv23Cc21R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ace712","type":"journal-article"},{"key":"xpvv-zv23Cc22R1","volume-title":"Molecular Fluids","author":"R.\u00a0B. 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All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"015422"}}