A NOTE ON SPECIAL CURVES IN E^4

Süha Yılmaz; Şuur Nizamoğlu

A NOTE ON SPECIAL CURVES IN E^4

Abstract

This article has consisted of a part of doctorate thesis by Süha Yılmaz [7]. Firstly, Frenet formulas are given in E^4.

Later, characterizations of regular and inclined curves are studied E^4. It has been given that a space-like curve is an inclined curve if and only if the

expression..........obtained using harmonic curvature functions in E^4. In addition, it has been observed that a fifth order vectorial differential equation of position vector of a space-like curve in E^4 been satisfied by means of Frenet formulas. Similarly, it has been denoted that a fourth order vectorial differential equation of tangent vector of a space-like curve in E^4 has been also verified using Frenet formulas. Moreover, we characterized tangent and trinormal indicatrices with one theorem. Finally, it has been denoted that if and only if spherical indicatrices of space-like curve with time-like trinormal vector are regular curves.

Keywords

Inclined curve,harmonic curvature,Frenet formulas,regular curve,space-like curve,time-like curve,spherical indicatrices

References

[1] Ekmekçi,N., Lorentz manifoldları üzerinde eğilim çizgileri, Doktora Tezi , A.Ü Fen Bilimleri Enstitüsü, 1991.
[2] Fox, L., Parker, I. B., Chebyshev Polynomials in Numerical Analysis, Oxford University Press, 1968.
[3] Gluck, H., Higher Curvatures of Curves in Euclidean Space, Proc.America.Math.Monthly, 73,699-704, 1966.
[4] O’Neill, B., Semi-Riemannian Geometry, Academic Press, NY, 1983.
[5] Şemin, F., Diferansiyel Geometri-I,İstanbul Üniversitesi Fen Fakültesi Yayınları, 1983.
[6] Turgut, A., 3-Boyutlu Minkowski Uzayında Space-Like ve Time-Like Regle Yüzeyler. A.Ü. Fen Bilimleri Enstitüsü, Doktora Tezi, 1995.
[7] Yılmaz , S., Spherical Indicators of Curves and Characterisations some Special Curves In Four Dimensional Lorentzian Space, Dokuz Eylül Üniversitesi Fen Bilimleri Enstitüsü, Doktora Tezi, 2001.
[8] Mağden, A., 𝑅4 Uzayında Bazı Özel Eğriler ve Karakterizasyonları, Atatürk Üniversitesi Fen Bilimleri Enstitüsü Doktora Tezi, 1990.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Süha Yılmaz ^*

Şuur Nizamoğlu This is me

Publication Date

June 30, 2016

Submission Date

March 10, 2016

Acceptance Date

-

Published in Issue

Year 2016 Volume: 2 Number: 1

IZ

https://izlik.org/JA96HN78UR

Cite

RIS / Bibtex

APA

Yılmaz, S., & Nizamoğlu, Ş. (2016). A NOTE ON SPECIAL CURVES IN E^4. Kirklareli University Journal of Engineering and Science, 2(1), 22-37. https://izlik.org/JA96HN78UR

AMA

1.Yılmaz S, Nizamoğlu Ş. A NOTE ON SPECIAL CURVES IN E^4. Kirklareli University Journal of Engineering and Science. 2016;2(1):22-37. https://izlik.org/JA96HN78UR

Chicago

Yılmaz, Süha, and Şuur Nizamoğlu. 2016. “A NOTE ON SPECIAL CURVES IN E^4”. Kirklareli University Journal of Engineering and Science 2 (1): 22-37. https://izlik.org/JA96HN78UR.

EndNote

Yılmaz S, Nizamoğlu Ş (June 1, 2016) A NOTE ON SPECIAL CURVES IN E^4. Kirklareli University Journal of Engineering and Science 2 1 22–37.

IEEE

[1]S. Yılmaz and Ş. Nizamoğlu, “A NOTE ON SPECIAL CURVES IN E^4”, Kirklareli University Journal of Engineering and Science, vol. 2, no. 1, pp. 22–37, June 2016, [Online]. Available: https://izlik.org/JA96HN78UR

ISNAD

Yılmaz, Süha - Nizamoğlu, Şuur. “A NOTE ON SPECIAL CURVES IN E^4”. Kirklareli University Journal of Engineering and Science 2/1 (June 1, 2016): 22-37. https://izlik.org/JA96HN78UR.

JAMA

1.Yılmaz S, Nizamoğlu Ş. A NOTE ON SPECIAL CURVES IN E^4. Kirklareli University Journal of Engineering and Science. 2016;2:22–37.

MLA

Yılmaz, Süha, and Şuur Nizamoğlu. “A NOTE ON SPECIAL CURVES IN E^4”. Kirklareli University Journal of Engineering and Science, vol. 2, no. 1, June 2016, pp. 22-37, https://izlik.org/JA96HN78UR.

Vancouver

1.Süha Yılmaz, Şuur Nizamoğlu. A NOTE ON SPECIAL CURVES IN E^4. Kirklareli University Journal of Engineering and Science [Internet]. 2016 Jun. 1;2(1):22-37. Available from: https://izlik.org/JA96HN78UR