Some characterizations of slant helices in the Euclidean space $E^n$

ALİ, Ahmad T.; TURGUT, Melih

Some characterizations of slant helices in the Euclidean space $E^n$

Ahmad T. ALİ, (King Abdul Aziz Univercity Faculty of Science, Department, of Mathematics, Jeddah, 21589, Saudi Arabia.)

Melih TURGUT (Dokuz Eylül Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, İzmir, Türkiye)

Hacettepe Journal of Mathematics and Statistics

5 0

Yıl: 2010 Cilt: 39 Sayı: 3 Sayfa Aralığı: 327 - 336 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Some characterizations of slant helices in the Euclidean space $E^n$

Öz:

In this work, the notion of a slant helix is extended to the space $Bbb {E}^ n$. First, we introduce the type-2 harmonic curvatures of a regular curve. Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space. We also express some integral characterizations of such curves in terms of the curvature functions. Finally, we give some characterizations of slant helices in terms of type-2 harmonic curvatures.

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Ali, A. Inclined curves in the Euclidean 5-space E5, J. Advanced Research in Pure Math. 1 (1), 15–22, 2009.
[2] Ali, A. and L´opez, R. Slant helices in Minkowski space E3 1, preprint, 2008: arXiv: 0810.1464v1 [math.DG].
[3] Ali, A. and L´opez, R. Timelike B2-slant helices in Minkowski space E4 1, Archivum Math. 46 (1), 39–46, 2010.
[4] Ali, A. Position vetors of slant helices in Euclidean 3-space, preprint, 2009: arXiv: 0907.0750v1 [math.DG].
[5] Barros, M. General helices and a theorem of Lancert, Proc. Amer. Math. Soc. 125, 1503– 1509, 1997.
[6] Camcı, Ç., İlarslan, K., Kula, L. and Hacısalihoğlu, H.H. Harmonic curvatures and gener- alized helices in En, Chaos, Solitons and Fractals 40, 2590–2596, 2009.
[7] Ekmek¸ci, N., Hacisalihoğlu, H.H. and ˙ Ilarslan, K. Harmonic curvatures in Lorentzian space, Bull. Malaysian Math. Soc. (Second Series) 23 (2), 173–179, 2000.
[8] Erdoğan, M. and Yılmaz, G. Null generalized and slant helices in 4-dimensional Lorentz- Minkowski space, Int. J. Contemp. Math. Sci. 3 (23), 1113–1120, 2008.
[9] Gluck, H. Higher curvatures of curves in Euclidean space, Amer. Math. Monthly 73, 699– 704, 1966.
[10] Izumiya, S. and Takeuchi, N. New special curves and developable surfaces, Turk. J. Math. 28 (2), 531–537, 2004.
[11] Kula, L. and Yayli, Y. On slant helix and its spherical indicatrix, Appl. Math. Comput. 169 (1), 600ˆu-607, 2005.
[12] Kula, L., Ekmekçi, N., Yayli Y. and İlarslan, K. Characterizations of slant helices in Eu- clidean 3-space, Turk. J. Math. 169 (1), 600ˆu-607, 2009.
[13] Milman, R. S. and Parker, G.D. Elements of Differential Geometry (Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1977).
[14] Monterde, J. Curves with constant curvature ratios, Bull. Mexican Math. Soc. Ser. 3A 13 (1), 177–186, 2007.
[15] Monterde, J. Salkowski curves revisted: A family of curves with constant curvature and non-constant torsion, Comput. Aided Geomet. 26, 271–278, 2009.
[16] Önder, M., Kazaz, M., Kocayiğit, H. and Kili¸c, O. B2-slant helix in Euclidean 4-space E4, Int. J. Contemp. Math. Sci. 3 (29), 1433–1440, 2008.
[17] Özdamar, E. and Hacisalihoğlu, H.H. A characterization of inclined curves in Euclidean n-space, Comm. Fac. Sci. Univ. Ankara, Ser. A1 24, 15–23, 1975.
[18] Öztürk, G., Arslan, K. and Hacisalihoglu, H.H. A characterization of ccr-curves in Rm, Proc. Estonian Acad. Sci. 57 (4), 217–224, 2008.
[19] Petrovic-Torgasev, M. and Sucurovic, E. W-curves in Minkowski spacetime, Novi. Sad. J. Math. 32 (2), 55–65, 2002.
[20] Scofield, P.D. Curves of constant precession, Amer. Math. Monthly 102, 531–537, 1995.
[21] Turgut, M. and Yilmaz, S. Characterizations of some special helices in E4, Sci. Magna. 4 (1), 51–55, 2008.
[22] Turgut, M. and Yilmaz, S. Some characterizations of type-3 slant helices in Minkowski space-time, Involve J. Math.2 (1), 115–120, 2009.

APA	ALİ A, TURGUT M (2010). Some characterizations of slant helices in the Euclidean space $E^n$. , 327 - 336.
Chicago	ALİ Ahmad T.,TURGUT Melih Some characterizations of slant helices in the Euclidean space $E^n$. (2010): 327 - 336.
MLA	ALİ Ahmad T.,TURGUT Melih Some characterizations of slant helices in the Euclidean space $E^n$. , 2010, ss.327 - 336.
AMA	ALİ A,TURGUT M Some characterizations of slant helices in the Euclidean space $E^n$. . 2010; 327 - 336.
Vancouver	ALİ A,TURGUT M Some characterizations of slant helices in the Euclidean space $E^n$. . 2010; 327 - 336.
IEEE	ALİ A,TURGUT M "Some characterizations of slant helices in the Euclidean space $E^n$." , ss.327 - 336, 2010.
ISNAD	ALİ, Ahmad T. - TURGUT, Melih. "Some characterizations of slant helices in the Euclidean space $E^n$". (2010), 327-336.

APA	ALİ A, TURGUT M (2010). Some characterizations of slant helices in the Euclidean space $E^n$. Hacettepe Journal of Mathematics and Statistics, 39(3), 327 - 336.
Chicago	ALİ Ahmad T.,TURGUT Melih Some characterizations of slant helices in the Euclidean space $E^n$. Hacettepe Journal of Mathematics and Statistics 39, no.3 (2010): 327 - 336.
MLA	ALİ Ahmad T.,TURGUT Melih Some characterizations of slant helices in the Euclidean space $E^n$. Hacettepe Journal of Mathematics and Statistics, vol.39, no.3, 2010, ss.327 - 336.
AMA	ALİ A,TURGUT M Some characterizations of slant helices in the Euclidean space $E^n$. Hacettepe Journal of Mathematics and Statistics. 2010; 39(3): 327 - 336.
Vancouver	ALİ A,TURGUT M Some characterizations of slant helices in the Euclidean space $E^n$. Hacettepe Journal of Mathematics and Statistics. 2010; 39(3): 327 - 336.
IEEE	ALİ A,TURGUT M "Some characterizations of slant helices in the Euclidean space $E^n$." Hacettepe Journal of Mathematics and Statistics, 39, ss.327 - 336, 2010.
ISNAD	ALİ, Ahmad T. - TURGUT, Melih. "Some characterizations of slant helices in the Euclidean space $E^n$". Hacettepe Journal of Mathematics and Statistics 39/3 (2010), 327-336.