{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T21:58:27Z","timestamp":1782338307686,"version":"3.54.5"},"reference-count":19,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,27]],"date-time":"2023-08-27T00:00:00Z","timestamp":1693094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSPD2023R749"],"award-info":[{"award-number":["RSPD2023R749"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, the quasi-frame and quasi-formulas are introduced in Galilean three-space. In addition, the quasi-Bertrand and the quasi-Mannheim curves are studied. It is proven that the angle between the tangents of two quasi-Bertrand or quasi-Mannhiem curves is not constant. Furthermore, the quasi-involute is studied. Moreover, we prove that there is no quasi-evolute curve in Galilean three-space. Also, we introduce quasi-Smarandache curves in Galilean three-space. Finally, we demonstrate an illustrated example to present our findings.<\/jats:p>","DOI":"10.3390\/axioms12090823","type":"journal-article","created":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T06:57:35Z","timestamp":1693205855000},"page":"823","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["On Some Quasi-Curves in Galilean Three-Space"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0288-2548","authenticated-orcid":false,"given":"Ayman","family":"Elsharkawy","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2878-4460","authenticated-orcid":false,"given":"Yusra","family":"Tashkandy","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6810-6640","authenticated-orcid":false,"given":"Walid","family":"Emam","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Noha","family":"Elsharkawy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gordon, B. (1979). A Simple Non-Euclidean Geometry and Its Physical Basis: An Elementary Account of Galilean Geometry and the Galilean Principle of Relativity, Springer.","DOI":"10.1007\/978-1-4612-6135-3"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"571","DOI":"10.2298\/TSCI22S2571K","article-title":"On tubular surfaces with modified orthogonal frame in Galilean space \ud835\udd3e3","volume":"26","author":"Mumcu","year":"2022","journal-title":"Therm. Sci."},{"key":"ref_3","first-page":"665","article-title":"Inelastic flows of curves according to equiform in Galilean space","volume":"24","author":"Yoon","year":"2011","journal-title":"J. Chungcheong Math. Soc."},{"key":"ref_4","first-page":"15","article-title":"Special Smarandache Curves with Respect to Darboux Frame in Galilean 3-Space","volume":"5","author":"Sahin","year":"2018","journal-title":"Int. J. Adv. Appl. Math. Mech."},{"key":"ref_5","first-page":"13","article-title":"Parallel Transports with respect to Frenet and Darboux Frames in the Galilean Space","volume":"1","author":"Sahin","year":"2020","journal-title":"J. Sci. Arts"},{"key":"ref_6","first-page":"75","article-title":"Involute-evolute curves in Galilean space \ud835\udd3e3","volume":"6","author":"Akyigit","year":"2010","journal-title":"Sci. Magna"},{"key":"ref_7","first-page":"467","article-title":"Special Smarandach curves according to the quasi frame in 4-dimensional Euclidean space E4","volume":"74","author":"Elsayied","year":"2021","journal-title":"Houst. J. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"17879","DOI":"10.3934\/math.2022985","article-title":"The non-linear Schr\u00f6dinger equation associated with the soliton surfaces in Minkowski 3-space","volume":"7","author":"Elsharkawy","year":"2022","journal-title":"AIMS Math."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Elshenhab, A.M., Moaaz, O., Dassios, I., and Elsharkawy, A. (2022). Motion along a space curve with a quasi-frame in Euclidean 3-space: Acceleration and Jerk. Symmetry, 14.","DOI":"10.3390\/sym14081610"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Hamouda, E., Moaaz, O., Cesarano, C., Askar, S., and Elsharkawy, A. (2022). Geometry of Solutions of the Quasi-Vortex Filament Equation in Euclidean 3-Space E3. Mathematics, 10.","DOI":"10.3390\/math10060891"},{"key":"ref_11","first-page":"229","article-title":"Bertrand curves for nonnull curves in 3-dimensional Lorentzian space","volume":"27","author":"Balgetir","year":"2004","journal-title":"Hadron. J."},{"key":"ref_12","first-page":"139","article-title":"Bertrand curves in Galilean space and their characterizations","volume":"32","author":"Oztekin","year":"2009","journal-title":"Kragujev. J. Math."},{"key":"ref_13","first-page":"69","article-title":"Weakened Bertrand curves in the Galilean space \ud835\udd3e3","volume":"2","author":"Oztekin","year":"2009","journal-title":"J. Adv. Math. Stud."},{"key":"ref_14","unstructured":"Boyer, C. (1968). A History of Mathematics, Wiley."},{"key":"ref_15","unstructured":"Hac\u0131salihoglu, H.H. (2000). Diferensiyel Geometri, Cilt I. Ankara \u00dcniversitesi, Fen Fak\u00fcltesi. Hac\u0131saliho\u011flu Yay\u0131nc\u0131l\u0131k."},{"key":"ref_16","first-page":"125","article-title":"Involute-evolute curve couples of higher order in Rn and their horizontal lifts in Rn","volume":"41","author":"Turgut","year":"1992","journal-title":"Commun. Fac. Sci. Univ. Ank. Ser. A"},{"key":"ref_17","first-page":"261","article-title":"On Mannheim partner curves in E3","volume":"4","author":"Orbay","year":"2009","journal-title":"Int. J. Phys. Sci."},{"key":"ref_18","first-page":"51","article-title":"Smarandache curves in Minkowski space-time","volume":"3","author":"Turgut","year":"2008","journal-title":"Int. J. Math. Comb."},{"key":"ref_19","first-page":"200","article-title":"Position vectors of curves in the Galilean space \ud835\udd3e3","volume":"64","author":"Ali","year":"2012","journal-title":"Mat. Vesn."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/9\/823\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:40:29Z","timestamp":1760128829000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/9\/823"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,27]]},"references-count":19,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["axioms12090823"],"URL":"https:\/\/doi.org\/10.3390\/axioms12090823","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,27]]}}}