Some special Smarandache curves according to the extended Darboux frame in $E_1^4$

Bahar Uyar Düldül

doi:10.26637/MJM0701/0014

Abstract

In this study, we define some special Smarandache curves according to the extended Darboux frame in Minkowski 4-space $E_1^4$ . We obtain the Frenet vectors and the curvatures of TD -Smarandache curve depending on the invariants of the extended Darboux frame of second kind.

Keywords:

Smarandache curve, extended Darboux frame field, Minkowski space

Mathematics Subject Classification:

Mathematics

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Bahar Uyar Düldül Yildiz Technical University, Education Faculty, Department of Mathematics and Science Education, Istanbul, Turkey.

Pages: 72-75
Date Published: 01-01-2019
Vol. 7 No. 01 (2019): Malaya Journal of Matematik (MJM)

Abdel-Aziz HS Saad MK. Computation of Smarandache curves according to Darboux frame in Minkowski 3space, Journal of the Egyptian Mathematical Society, 25(4)(2017), 382-390.

Ali AT. Special Smarandache curves in the Euclidean space, International Journal of Mathematical Combinatorics, 2(2010), 30-36.

Çetin M, Tunçer Y. Karacan MK. Smarandache curves according to Bishop frame in Euclidean 3-space, Gen. Math. Notes, 20(2)(2014), 50-66.

Elzawy M. Smarandache curves in Euclidean 4- space $E^4$, Journal of the Egyptian Mathematical Society, 25(2017), 268-271.

Gürses N. Bektaş Ö. Yüce S. Special Smarandache curves in $mathbb{R}_1^3$, Commun. Fac. Sci. Univ. Ank. Sér. Al Math. Stat., 65(2)(2016), 143-160.

O'Neill B. Semi Riemannian Geometry. Academic Press, New York-London, 1983.

Turgut M. Yılmaz S. Smarandache curves in Minkowski space-time, International Journal of Mathematical Combinatorics, 3(2008), 51-55.

Uyar Düldül B. Extended Darboux frame field in Minkowski space-time $mathbb{E}_1^4$, Malaya Journal of Matematik, 6(3)(2018), 473-477.

Yilmaz S. Turgut M. On the differential geometry of the curves in Minkowski space-time I, Int. J. Contemp. Math. Sciences, 3(27)(2008), 1343-1349.

Yilmaz S. Savci ÜZ. Smarandache curves and applications according to type-2 Bishop frame in Euclidean 3space, International Journal of Mathematical Combinatorics, 2(2016), 1-15.