Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, , 107 - 113, 30.09.2021
https://doi.org/10.32323/ujma.937479

Öz

Kaynakça

  • M. P. Do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Courier Dover Publications, 2016.
  • A. N. Pressley, Elementary Differential Geometry, Springer Science & Business Media, 2010. B.Y. Chen, When does the position vector of a space curve always lie in its rectifying plane? Amer. Math. Month., 110(2) (2003), 147–152.
  • B.Y. Chen, F. Dillen, Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Acad. Sinica, 33(2) (2005), 77-90.
  • B.Y. Chen, Rectifying curves and geodesics on a cone in the Euclidean 3-space, Tamkang J. Math., 48(2) (2017), 209-214.
  • S. Deshmukh, B.Y. Chen, S. Alshamari, On rectifying curves in Euclidean 3-space, Turk. J. Math., 42(2) (2018), 609-620.
  • K. {\.I}larslan, E. Nesovic, Some characterizations of rectifying curves in the Euclidean space $\mathbf{E}^4$, Turk. J. Math., 32(1) (2008), 21-30.
  • S. Cambie, W. Goemans, I. Van den Bussche, Rectifying curves in the $n$-dimensional Euclidean space,Turk. J. Math., 40(1) (2016), 210-223.
  • P. Lucas, J.A. Ortega-Yag{\"u}es, Rectifying curves in the three-dimensional sphere, J. Math. Anal. Appl., 421(2) (2015), 1855-1868.
  • P. Lucas, J.A. Ortega-Yag{\"u}es, Rectifying curves in the three-dimensional hyperbolic space, Medit. J. Math., 13(4) (2016), 2199-2214.
  • K. Ilarslan, E. Ne\v{s}ovi\'{c}, T. M. Petrovi\'{c}, Some characterization of rectifying curves in the Minkowski 3-Space, Novi Sad J. Math., 33(2) (2003), 23-32.
  • K. Ilarslan, E. Ne\v{s}ovi\'{c}, On rectifying curves as centrodes and extremal curves in the Minkowski 3-Space, Novi Sad J. Math., 37(1) (2007), 53-64.
  • K. Ilarslan, E. Ne\v{s}ovi\'{c}, Some characterizations of null, pseudo null and partially null rectifying curves in Minkowski space-time, Taiwanese J. Math., 12(5) (2008), 1035-1044.
  • T.A. Ali, M. Onder, Some characterizations of space-like rectifying curves in the Minkowski space-time, Glob. J. Sci. Fron. Res. Math. Des. Sci., 12(1) (2012), 57-63.
  • K. Ilarslan, E. Ne\v{s}ovi\'{c}, Some relations between normal and rectifying curves in Minkowski space-time, Inter. Elec. J. Geom., 7(1) (2014), 26-35.
  • F. Hathout, A new class of curves generalizing helix and rectifying curves, arXiv: Diff. Geom., (2018).
  • Z. Iqbal, J. Sengupta, Non-null (spacelike or timelike) f-rectifying curves in the Minkowski 3-space $\mathbb{E}_1^3$, Eurasian Bul. Math., 3(1) (2020), 38-55.
  • Z. Iqbal, J. Sengupta, Null (lightlike) f-rectifying curves in the Minkowski 3-space $\mathbb{E}_1^3$, Fundam. J. Math. Appl., 3(1) (2020), 8-16.
  • Z. Iqbal, J. Sengupta, Differential geometric aspects of lightlike $f$-rectifying curves in Minkowski space-time, Diff. Geom. - Dyn. Syst., 22 (2020), 113-129. Z. Iqbal, J. Sengupta, On $f$-Rectifying Curves in the Euclidean 4-Space, Acta Univ. Sapientiae Matem. (Accepted Manuscript).
  • H. Gluck, Higher curvatures of curves in Euclidean space, Amer. Math. Mon., 73(7) (1966), 699--704.
  • H. Gluck, Higher curvatures of curves in Euclidean space II, Amer. Math. Mon., 74(9) (1967), 1049--1056.

A Study on $f$-Rectifying Curves in Euclidean $n$-Space

Yıl 2021, , 107 - 113, 30.09.2021
https://doi.org/10.32323/ujma.937479

Öz

A rectifying curve in the Euclidean $n$-space $\mathbb{E}^n$ is defined as an arc-length parametrized curve $\gamma$ in $\mathbb{E}^n$ such that its position vector always lies in its rectifying space (i.e., the orthogonal complement of its principal normal vector field) in $\mathbb{E}^n$. In this paper, in analogy to this, we introduce the notion of an $f$-rectifying curve in $\mathbb{E}^n$ as a curve $\gamma$ in $\mathbb{E}^n$ parametrized by its arc-length $s$ such that its $f$-position vector field $\gamma_f$, defined by $\gamma_f(s) = \int f(s) d\gamma$, always lies in its rectifying space in $\mathbb{E}^n$, where $f$ is a nowhere vanishing real-valued integrable function in parameter $s$. The main purpose is to characterize and classify such curves in $\mathbb{E}^n$.

Kaynakça

  • M. P. Do Carmo, Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition, Courier Dover Publications, 2016.
  • A. N. Pressley, Elementary Differential Geometry, Springer Science & Business Media, 2010. B.Y. Chen, When does the position vector of a space curve always lie in its rectifying plane? Amer. Math. Month., 110(2) (2003), 147–152.
  • B.Y. Chen, F. Dillen, Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Acad. Sinica, 33(2) (2005), 77-90.
  • B.Y. Chen, Rectifying curves and geodesics on a cone in the Euclidean 3-space, Tamkang J. Math., 48(2) (2017), 209-214.
  • S. Deshmukh, B.Y. Chen, S. Alshamari, On rectifying curves in Euclidean 3-space, Turk. J. Math., 42(2) (2018), 609-620.
  • K. {\.I}larslan, E. Nesovic, Some characterizations of rectifying curves in the Euclidean space $\mathbf{E}^4$, Turk. J. Math., 32(1) (2008), 21-30.
  • S. Cambie, W. Goemans, I. Van den Bussche, Rectifying curves in the $n$-dimensional Euclidean space,Turk. J. Math., 40(1) (2016), 210-223.
  • P. Lucas, J.A. Ortega-Yag{\"u}es, Rectifying curves in the three-dimensional sphere, J. Math. Anal. Appl., 421(2) (2015), 1855-1868.
  • P. Lucas, J.A. Ortega-Yag{\"u}es, Rectifying curves in the three-dimensional hyperbolic space, Medit. J. Math., 13(4) (2016), 2199-2214.
  • K. Ilarslan, E. Ne\v{s}ovi\'{c}, T. M. Petrovi\'{c}, Some characterization of rectifying curves in the Minkowski 3-Space, Novi Sad J. Math., 33(2) (2003), 23-32.
  • K. Ilarslan, E. Ne\v{s}ovi\'{c}, On rectifying curves as centrodes and extremal curves in the Minkowski 3-Space, Novi Sad J. Math., 37(1) (2007), 53-64.
  • K. Ilarslan, E. Ne\v{s}ovi\'{c}, Some characterizations of null, pseudo null and partially null rectifying curves in Minkowski space-time, Taiwanese J. Math., 12(5) (2008), 1035-1044.
  • T.A. Ali, M. Onder, Some characterizations of space-like rectifying curves in the Minkowski space-time, Glob. J. Sci. Fron. Res. Math. Des. Sci., 12(1) (2012), 57-63.
  • K. Ilarslan, E. Ne\v{s}ovi\'{c}, Some relations between normal and rectifying curves in Minkowski space-time, Inter. Elec. J. Geom., 7(1) (2014), 26-35.
  • F. Hathout, A new class of curves generalizing helix and rectifying curves, arXiv: Diff. Geom., (2018).
  • Z. Iqbal, J. Sengupta, Non-null (spacelike or timelike) f-rectifying curves in the Minkowski 3-space $\mathbb{E}_1^3$, Eurasian Bul. Math., 3(1) (2020), 38-55.
  • Z. Iqbal, J. Sengupta, Null (lightlike) f-rectifying curves in the Minkowski 3-space $\mathbb{E}_1^3$, Fundam. J. Math. Appl., 3(1) (2020), 8-16.
  • Z. Iqbal, J. Sengupta, Differential geometric aspects of lightlike $f$-rectifying curves in Minkowski space-time, Diff. Geom. - Dyn. Syst., 22 (2020), 113-129. Z. Iqbal, J. Sengupta, On $f$-Rectifying Curves in the Euclidean 4-Space, Acta Univ. Sapientiae Matem. (Accepted Manuscript).
  • H. Gluck, Higher curvatures of curves in Euclidean space, Amer. Math. Mon., 73(7) (1966), 699--704.
  • H. Gluck, Higher curvatures of curves in Euclidean space II, Amer. Math. Mon., 74(9) (1967), 1049--1056.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Zafar Iqbal

Joydeep Sengupta

Yayımlanma Tarihi 30 Eylül 2021
Gönderilme Tarihi 15 Mayıs 2021
Kabul Tarihi 1 Ekim 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Iqbal, Z., & Sengupta, J. (2021). A Study on $f$-Rectifying Curves in Euclidean $n$-Space. Universal Journal of Mathematics and Applications, 4(3), 107-113. https://doi.org/10.32323/ujma.937479
AMA Iqbal Z, Sengupta J. A Study on $f$-Rectifying Curves in Euclidean $n$-Space. Univ. J. Math. Appl. Eylül 2021;4(3):107-113. doi:10.32323/ujma.937479
Chicago Iqbal, Zafar, ve Joydeep Sengupta. “A Study on $f$-Rectifying Curves in Euclidean $n$-Space”. Universal Journal of Mathematics and Applications 4, sy. 3 (Eylül 2021): 107-13. https://doi.org/10.32323/ujma.937479.
EndNote Iqbal Z, Sengupta J (01 Eylül 2021) A Study on $f$-Rectifying Curves in Euclidean $n$-Space. Universal Journal of Mathematics and Applications 4 3 107–113.
IEEE Z. Iqbal ve J. Sengupta, “A Study on $f$-Rectifying Curves in Euclidean $n$-Space”, Univ. J. Math. Appl., c. 4, sy. 3, ss. 107–113, 2021, doi: 10.32323/ujma.937479.
ISNAD Iqbal, Zafar - Sengupta, Joydeep. “A Study on $f$-Rectifying Curves in Euclidean $n$-Space”. Universal Journal of Mathematics and Applications 4/3 (Eylül 2021), 107-113. https://doi.org/10.32323/ujma.937479.
JAMA Iqbal Z, Sengupta J. A Study on $f$-Rectifying Curves in Euclidean $n$-Space. Univ. J. Math. Appl. 2021;4:107–113.
MLA Iqbal, Zafar ve Joydeep Sengupta. “A Study on $f$-Rectifying Curves in Euclidean $n$-Space”. Universal Journal of Mathematics and Applications, c. 4, sy. 3, 2021, ss. 107-13, doi:10.32323/ujma.937479.
Vancouver Iqbal Z, Sengupta J. A Study on $f$-Rectifying Curves in Euclidean $n$-Space. Univ. J. Math. Appl. 2021;4(3):107-13.

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