On generalized osculating-type curves in Myller configuration

Zehra İşbilir; Murat Tosun

doi:10.2478/auom-2024-0020

.blurhash-client-img { display: none !important; }

On generalized osculating-type curves in Myller configuration

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 32 (2024): Issue 2 (June 2024)

By: Zehra İşbilir and Murat Tosun

Open Access

|Jul 2024

Abstract

In this study, we examine osculating-type curves with Frenet-type frame in Myller configuration for Euclidean 3-space E₃. We present the necessary characterizations for a curve to be an osculating-type curve. Characterizations originating from the natural structure of Myller configuration are a generalization of osculating curves according to the Frenet frame. Also, we introduce some new results that are not valid for osculating curves. Then, we give an illustrative numerical example supported by a figure.

References

S. Breuer, D. Gottlieb, Explicit characterization of spherical curves, Proc. Amer. Math. Soc., 27(1) (1971), 126–127.
Search in Google Scholar Back to article
B.-Y. Chen, When does the position vector of a space curve always lie in its rectifying plane? Amer. Math. Monthly, 110(2) (2003), 147–152.
Search in Google Scholar Back to article
B.-Y. Chen, F. Dillen, Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Academia Sinica, 33(2) (2005), 77–90.
Search in Google Scholar Back to article
B.-Y. Chen, Rectifying curves and geodesics on a cone in the Euclidean 3-space, Tamkang J. Math., 48(2) (2017), 209-–214.
Search in Google Scholar Back to article
S. Deshmukh, B.-Y. Chen, S. H. Alshammari, On rectifying curves in Euclidean 3-space, Turk. J. Math., 42(2) (2018), 609-–620.
Search in Google Scholar Back to article
F. Frenet, Sur les courbesá double courbure, J. Math. Pures Appl., (1852), 437–447.
Search in Google Scholar Back to article
B. Heroiu, Versor fields along a curve in a four dimensional Lorentz space, J. Adv. Math. Stud., 4(1) (2011), 49–57.
Search in Google Scholar Back to article
K. İlarslan, E. Nešović, M. Petrovic-Torgasev, Some characterizations of rectifying curves in the Minkowski 3-space, Novi Sad J. Math., 33(2) (2003), 23–32.
Search in Google Scholar Back to article
K. İlarslan, E. Nešović, Timelike and null normal curves in Minkowski space 𝔼³₁, Indian J. Pure Appl. Math., 35(7) (2004), 881–888.
Search in Google Scholar Back to article
K. İlarslan, Spacelike normal curves in Minkowski space 𝔼³₁, Turk. J. Math., 29(2) (2005), 53–63.
Search in Google Scholar Back to article
K. İlarslan, E. Nešović, On rectifying curves as centrodes and extremal curves in the Minkowski 3-space, Novi Sad J. Math., 37(1) (2007), 53–64.
Search in Google Scholar Back to article
K. İlarslan, E. Nešović, Some characterizations of rectifying curves in the Euclidean space E⁴, Turk. J. Math., 32(1) (2008), 21–30.
Search in Google Scholar Back to article
K. İlarslan, E. Nešović, Some characterizations of null, pseudo null and partially null rectifying curves in Minkowski space-time, Taiwan. J. Math., 12(5) (2008), 1035–1044.
Search in Google Scholar Back to article
K. İlarslan, E. Nešović, Some characterizations of osculating curves in the Euclidean spaces, Demonstr. Math., 41(4) (2008), 931–940.
Search in Google Scholar Back to article
K. İlarslan, E. Nešović, Spacelike and timelike normal curves in Minkowski space-time, Publ. Inst. Math., 105 (2009), 111–118.
Search in Google Scholar Back to article
K. İlarslan, E. Nešović, The first kind and the second kind osculating curves in Minkowski space-time, Compt. Rend. Acad. Bulg. Sci., 62(6) (2009), 677–686.
Search in Google Scholar Back to article
K. İlarslan, E. Nešović, Some relations between normal and rectifying curves in Minkowski space-time, Int. Electron. J. Geom., 7(1) (2014), 26–35.
Search in Google Scholar Back to article
K. İlarslan, E. Nešović, Some characterizations of pseudo and partially null osculating curves in Minkowski space-time, Int. Electron. J. Geom., 4(2) (2011), 1–12.
Search in Google Scholar Back to article
Z. İşbilir, M. Tosun, Osculating-type curves with Myller configuration in Euclidean 4-space, (submitted).
Search in Google Scholar Back to article
Z. İşbilir, M. Tosun, A new insight on rectifying-type curves in Euclidean 4-space, Int. Electron. J. Geom., 16(2) (2023), 644-652.
Search in Google Scholar Back to article
Z. İşbilir, M. Tosun, Generalized Smarandache curves with Frenet-type frame, Honam Math. J., 46(2) (2024), 181-197.
Search in Google Scholar Back to article
Ö. Keskin, Y. Yaylı, Rectifying-type curves and rotation minimizing frame ℝⁿ, arXiv Preprint, arXiv:1905.04540, (2019).
Search in Google Scholar Back to article
G. F. Macsim, A. Mihai, A. Olteanu, Special curves in a Myller configuration, Proceedings of the 16th Workshop on Mathematics, Computer Science and Technical Education, Department of Mathematics and Computer Science, 2 (2019), 78–84.
Search in Google Scholar Back to article
G. F. Macsim, A. Mihai, A. Olteanu, On rectifying-type curves in a Myller configuration, Bull. Korean Math. Soc., 56(2) (2019), 383–390.
Search in Google Scholar Back to article
G. F. Macsim, A. Mihai, A. Olteanu, Curves in a Myller configuration, International Conference on Applied and Pure Mathematics (ICAPM 2017), Ia¸si, November 2-5, 2017.
Search in Google Scholar Back to article
R. Miron, Geometria unor configurat¸ii Myller, Analele S¸t. Univ., VI(3) (1960).
Search in Google Scholar Back to article
R. Miron, The Geometry of Myller Configurations. Applications to Theory of Surfaces and Nonholonomic Manifolds, Romanian Academy, (2010).
Search in Google Scholar Back to article
T. Otsuki, Di erential Geometry, Asakura Publishing Co. Ltd. Tokyo (1961).
Search in Google Scholar Back to article
J. A. Serret, Sur quelques formules relatives à la théorie des courbes à double courbure, J. Math. Pures Appl., (1851), 193–207.
Search in Google Scholar Back to article
E. M. Solouma, Characterization of Smarandache trajectory curves of constant mass point particles as they move along the trajectory curve via PAF, Bull. Math. Anal. Appl., 13(4) (2021), 14–30.
Search in Google Scholar Back to article
Y. C. Wong, A global formulation of the condition for a curve to lie in a sphere, Monatsh. Math., 67 (1963), 363–365.
Search in Google Scholar Back to article
Y. C. Wong, On an explicit characterization of spherical curves, Proceedings of the American Math. Soc., 34(1) (1972), 239–242.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2024-0020 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 85 - 98

Submitted on: Jul 29, 2023

Published on: Jul 10, 2024

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Myller configuration,

osculating-type curve,

versor field

Related subjects:

Mathematics,

General mathematics

© 2024 Zehra İşbilir, Murat Tosun, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 32 (2024): Issue 2 (June 2024)