{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T23:04:04Z","timestamp":1762211044167},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T00:00:00Z","timestamp":1672099200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T00:00:00Z","timestamp":1672099200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s00500-022-07741-1","type":"journal-article","created":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T03:02:30Z","timestamp":1672110150000},"page":"2159-2169","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An approach to characterizations of null curves lying in timelike ruled surfaces"],"prefix":"10.1007","volume":"27","author":[{"given":"Cumali","family":"Ekici","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Talat","family":"K\u00f6rp\u0131nar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasin","family":"\u00dcnl\u00fct\u00fcrk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,12,27]]},"reference":[{"key":"7741_CR1","doi-asserted-by":"crossref","unstructured":"Abal\u0131 B, Y\u00fccesan A (2022) Associated curves of a Frenet curve in the dual Lorentzian space. Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 71(1):285\u2013304 (2022)","DOI":"10.31801\/cfsuasmas.877170"},{"issue":"3","key":"7741_CR2","first-page":"551","volume":"42","author":"RA Abdel-Baky","year":"2020","unstructured":"Abdel-Baky RA, \u00dcnl\u00fct\u00fcrk Y (2020) A new construction of timelike ruled surfaces with constant Disteli-axis. Honam Math J 42(3):551\u2013568","journal-title":"Honam Math J"},{"issue":"10","key":"7741_CR3","doi-asserted-by":"publisher","first-page":"17843","DOI":"10.3934\/math.2022983","volume":"7","author":"MT Aldossary","year":"2022","unstructured":"Aldossary MT, Abdel-Baky RA (2022) On the Blaschke approach of Bertrand offsets of spacelike ruled surfaces. AIMS Math. 7(10):17843\u201317858","journal-title":"AIMS Math."},{"key":"7741_CR4","doi-asserted-by":"publisher","first-page":"749","DOI":"10.3390\/sym14040749","volume":"14","author":"N Alluhaibi","year":"2022","unstructured":"Alluhaibi N, Abdel-Baky RA (2022) Kinematic geometry of timelike ruled surfaces in Minkowski 3-Space $${\\mathbb{E} }_{1}^{3}$$. Symmetry 14:749","journal-title":"Symmetry"},{"issue":"3","key":"7741_CR5","doi-asserted-by":"publisher","first-page":"635","DOI":"10.4134\/BKMS.2012.49.3.635","volume":"49","author":"N Ayy\u0131ld\u0131z","year":"2012","unstructured":"Ayy\u0131ld\u0131z N, Turhan T (2012) A study on a ruled surface with lightlike ruling for a null curve with Cartan frame. Bull Korean Math Soc 49(3):635\u2013645","journal-title":"Bull Korean Math Soc"},{"issue":"2","key":"7741_CR6","first-page":"112","volume":"62","author":"N Ayy\u0131ld\u0131z","year":"2000","unstructured":"Ayy\u0131ld\u0131z N, \u00c7\u00f6ken AC, K\u0131l\u0131\u00e7 A (2000) Differential-geometrical conditions between curves and semi-ruled surfaces in the semi-Euclidean spaces. Tensor N S 62(2):112\u2013119","journal-title":"Tensor N S"},{"issue":"1","key":"7741_CR7","first-page":"1","volume":"7","author":"N Ayy\u0131ld\u0131z","year":"2001","unstructured":"Ayy\u0131ld\u0131z N, \u00c7\u00f6ken AC, Y\u00fccesan A (2001) Differential-geometrical conditions between geodesic curves and ruled surfaces in the Lorentz space. Balk J Geo Appl 7(1):1\u201312","journal-title":"Balk J Geo Appl"},{"key":"7741_CR8","unstructured":"Blaschke W (1930) Vorlesungen \u00fcber differential geometrie I, Ban I. Verlag Von Julius Springer-Verlag, Berlin"},{"key":"7741_CR9","first-page":"229","volume":"20","author":"WB Bonnor","year":"1969","unstructured":"Bonnor WB (1969) Null curves in Minkowski space-time. Tensor 20:229\u2013242","journal-title":"Tensor"},{"issue":"1","key":"7741_CR10","first-page":"111","volume":"2","author":"AC \u00c7\u00f6ken","year":"2007","unstructured":"\u00c7\u00f6ken AC, \u00c7ift\u00e7i \u00dc (2007) On null curves on surfaces and null vectors in Lorentz space. S\u00fcleyman Demirel \u00dcniver Edeb Fak\u00fcltesi Fen Dergisi 2(1):111\u2013116","journal-title":"S\u00fcleyman Demirel \u00dcniver Edeb Fak\u00fcltesi Fen Dergisi"},{"issue":"1A","key":"7741_CR11","first-page":"21","volume":"35","author":"AC \u00c7\u00f6ken","year":"2008","unstructured":"\u00c7\u00f6ken AC, \u00c7ift\u00e7i \u00dc, Ekici C (2008) On parallel timelike ruled surfaces with timelike rulings. Kuwait J Sci Eng 35(1A):21\u201332","journal-title":"Kuwait J Sci Eng"},{"key":"7741_CR12","doi-asserted-by":"crossref","unstructured":"Duggal KL, Jin DH (2007) Null curves and hypersurfaces of semi-Riemannian manifolds, World Scientific Publishing Co. Pte. Ltd, Singapore","DOI":"10.1142\/6449"},{"issue":"1","key":"7741_CR13","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.jmaa.2012.03.014","volume":"393","author":"C Ekici","year":"2012","unstructured":"Ekici C, \u00c7\u00f6ken AC (2012) The integral invariants of parallel timelike ruled surfaces. JMAA-J Math Anal Appl 393(1):97\u2013107","journal-title":"JMAA-J Math Anal Appl"},{"issue":"1A","key":"7741_CR14","first-page":"19","volume":"39","author":"C Ekici","year":"2012","unstructured":"Ekici C, \u00d6z\u00fcsa\u011flam E (2012) On the method of determination of a developable timelike ruled surface. KJSE-Kuwait J Sci Eng 39(1A):19\u201341","journal-title":"KJSE-Kuwait J Sci Eng"},{"issue":"5","key":"7741_CR15","doi-asserted-by":"publisher","first-page":"1561","DOI":"10.3906\/mat-1909-6","volume":"44","author":"SM Gilani","year":"2020","unstructured":"Gilani SM, Abazari N, Yayli Y (2020) Characterizations of dual curves and dual focal curves in dual Lorentzian space $${\\mathbb{D} }_{1}^{3}$$. Turk J Math 44(5):1561\u20131577","journal-title":"Turk J Math"},{"key":"7741_CR16","volume-title":"Differential geometry","author":"HW Guggenheimer","year":"1963","unstructured":"Guggenheimer HW (1963) Differential geometry. Mc. Graw-Hill Book Company, New York"},{"issue":"3","key":"7741_CR17","doi-asserted-by":"publisher","first-page":"2114","DOI":"10.3934\/math.2021129","volume":"6","author":"R Makki","year":"2021","unstructured":"Makki R (2021) Some characterizations of non-null rectifying curves in dual Lorentzian 3-space $${\\mathbb{D} }_{1}^{3}$$. AIMS Math 6(3):2114\u20132131","journal-title":"AIMS Math"},{"key":"7741_CR18","doi-asserted-by":"publisher","unstructured":"Naghi MF, Abdel-Baky RA, Mofarreh F (2022) Time-like ruled surface in one-parameter hyperbolic dual spherical motions. Abstr Appl Anal 2022:9323490. https:\/\/doi.org\/10.1155\/2022\/9323490","DOI":"10.1155\/2022\/9323490"},{"issue":"1","key":"7741_CR19","first-page":"53","volume":"16","author":"\u015e Nizamo\u011flu","year":"1993","unstructured":"Nizamo\u011flu \u015e, G\u00fclp\u0131nar N (1993) Differential-geometrical conditions between curves and ruled surfaces. J Fac Sci Ege Univer 16(1):53\u201362","journal-title":"J Fac Sci Ege Univer"},{"key":"7741_CR20","unstructured":"O\u2019Neill B (1983) Semi-Riemannian geometry with applications to relativity. Academic Press, London"},{"key":"7741_CR21","unstructured":"Pasinli \u00d6 (1997) Ruled surfaces. Master thesis, Grad. Sch. Nat. Appl. Sci. Dokuz Eyl\u00fcl Uni., \u0130zmir"},{"issue":"1","key":"7741_CR22","first-page":"67","volume":"16","author":"\u00dc Pekmen","year":"1995","unstructured":"Pekmen \u00dc (1995) Differential-geometrical conditions between geodesic curves and ruled surfaces. J Fac Sci Ege Univer 16(1):67\u201374","journal-title":"J Fac Sci Ege Univer"},{"key":"7741_CR23","unstructured":"\u015ei\u015fman M (1995) Differential geometrical conditions between curvature and osculating strip curves and ruled surfaces. Master thesis, Grad. Sch. Nat. Appl. Sci. Dokuz Eyl\u00fcl Uni., \u0130zmir"},{"key":"7741_CR24","volume-title":"Die geometrie der dynamen","author":"E Study","year":"1933","unstructured":"Study E (1933) Die geometrie der dynamen. Verlag Teubner, Leipzig"},{"key":"7741_CR25","volume-title":"Darboux ani d\u00f6nme vekt\u00f6rleri ile spacelike ve timelike y\u00fczeyler geometrisi","author":"HH U\u011furlu","year":"2012","unstructured":"U\u011furlu HH, \u00c7al\u0131\u015fkan A (2012) Darboux ani d\u00f6nme vekt\u00f6rleri ile spacelike ve timelike y\u00fczeyler geometrisi. CB\u00dc Yay, Manisa ((in Turkish))"},{"issue":"1","key":"7741_CR26","first-page":"185","volume":"41","author":"Y \u00dcnl\u00fct\u00fcrk","year":"2019","unstructured":"\u00dcnl\u00fct\u00fcrk Y, Y\u0131lmaz S, Ekici C (2019) The relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space $${\\mathbb{D}}_{1}^{3}$$. Honam Math J 41(1):185\u2013195","journal-title":"Honam Math J"},{"key":"7741_CR27","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/0094-114X(76)90006-9","volume":"11","author":"GR Veldkamp","year":"1976","unstructured":"Veldkamp GR (1976) On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics. Mech Math Theory 11:141\u2013156","journal-title":"Mech Math Theory"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07741-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-022-07741-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07741-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,16]],"date-time":"2023-02-16T15:12:30Z","timestamp":1676560350000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-022-07741-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,27]]},"references-count":27,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["7741"],"URL":"https:\/\/doi.org\/10.1007\/s00500-022-07741-1","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,27]]},"assertion":[{"value":"11 December 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 December 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}