{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T09:26:30Z","timestamp":1762075590446,"version":"build-2065373602"},"reference-count":10,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,18]],"date-time":"2022-11-18T00:00:00Z","timestamp":1668729600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>We start by introducing and studying two sequences of curvatures provided by the higher-order derivatives of the usual Frenet equation of a given plane curve C. These curvatures are expressed by a recurrence starting with the pair (0,\u2212k) where k is the classical curvature function of C. Moreover, for the space curves, we succeed in introducing three recurrent sequences of curvatures starting with the triple (\u2212k,0,\u03c4). Some kinds of helices of a higher order are defined.<\/jats:p>","DOI":"10.3390\/a15110436","type":"journal-article","created":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T04:13:36Z","timestamp":1669004016000},"page":"436","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Higher-Order Curvatures of Plane and Space Parametrized Curves"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5230-2751","authenticated-orcid":false,"given":"Mircea","family":"Crasmareanu","sequence":"first","affiliation":[{"name":"Faculty of Mathematics, University \u201cAlexandru Ioan Cuza\u201d, 700506 Iasi, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1090\/S0273-0979-1983-15187-X","article-title":"The influence of elasticity on analysis: The classic heritage","volume":"9","author":"Truesdell","year":"1983","journal-title":"Bull. Am. Math. Soc. New Ser."},{"key":"ref_2","first-page":"50","article-title":"A note on the hyperbolic curvature of Euclidean plane curves","volume":"12","author":"Crasmareanu","year":"2022","journal-title":"Rom. J. Math. Comput. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Alencar, H., Santos, W., and Silva Neto, G. (2022). Differential Geometry of Plane Curves, American Mathematical Society. Student Mathematical Library 96.","DOI":"10.1090\/stml\/096"},{"key":"ref_4","first-page":"303","article-title":"The generalized radial curvature of plane curves","volume":"15","author":"Crasmareanu","year":"2022","journal-title":"J. Adv. Math. Stud."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"De Faria, E., and De Melo, W. (2008). Mathematical Tools for One-Dimensional Dynamics, Cambridge University Press.","DOI":"10.1017\/CBO9780511755231"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1550111","DOI":"10.1142\/S021988781550111X","article-title":"Unitary vector fields are Fermi-Walker transported along Rytov-Legendre curves","volume":"12","author":"Crasmareanu","year":"2015","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00022-021-00610-6","article-title":"Sequential natural mates of Frenet curves in Euclidean 3-space","volume":"112","author":"Camci","year":"2021","journal-title":"J. Geom."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1017\/S0004972712000809","article-title":"Slant curves and particles in three-dimensional warped products and their Lancret invariants","volume":"88","author":"Calin","year":"2013","journal-title":"Bull. Aust. Math. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s10659-019-09755-7","article-title":"Boundary value problems for Euler-Bernoulli planar elastica. A solution construction procedure","volume":"139","author":"Arroyo","year":"2020","journal-title":"J. Elasticity"},{"key":"ref_10","first-page":"27","article-title":"Extremals of the generalized Euler-Bernoulli energy and applications","volume":"12","author":"Garay","year":"2008","journal-title":"J. Geom. Symmetry Phys."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/11\/436\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:21:41Z","timestamp":1760145701000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/11\/436"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,18]]},"references-count":10,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["a15110436"],"URL":"https:\/\/doi.org\/10.3390\/a15110436","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2022,11,18]]}}}