Yıl: 2000 Cilt: 49 Sayı: 1-2 Sayfa Aralığı: 15 - 23 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

On harmonic curvatures of a Frenet curve

Öz:
In this paper we consider harmonic curvatures of a Frenet curve of osculating order d. We also consider a general helix of AW(k) type where k=l,2 and 3. We have show that, there is no general helix of AW(3)type. We also show that, a general helix of rank 1 and of AW(3) type must be a circular helix. We give curvature conditions of the curves, which have AW(2) property. In the final part, we visualize the plane and space curves of (weak) AW(2)type.
Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık
Belge Türü: Makale Makale Türü: Diğer Erişim Türü: Erişime Açık
  • [1] Arslan, K. and West, A., Product Submanifolds with Pointwise 3-Planar Nonnal Sections, Glasgow Math. J. 37,(1995), 73-81.
  • [2] Dillen F., The Classification of Hypersurfaces of a Euclidean Space with Parallel Higher Order Fundamental Form. Math Z. 203(1990), 635-643.
  • [3] Dillen, F. and Nölker, S., Semi-parallelity, multy-rotation surfaces and the helix-property, J. Reine Angew. Math. 435,(1993), 33-63.
  • [4] Ferus, D. and Schirrmacher, S., Submanifolds in Euclidean Space with Simple Geodesies, Math. Ann. 260 (1982), 57-62.
  • [5] Gray, Alfred., Modem Differential Geometry of Curves and Surfaces, CRS Press, 1993.
  • [6] Hacisalihoğlu, H.H., Diferensiyel Geometri, Ankara Üniversitesi Fen Fakültesi,1993.
  • [7] Ross, S.L., Differential Equations, Second Edition, John Wiley&Sons Inc., 1974.
APA ARSLAN K, ÇELİK Y, HACISALİHOĞLU H (2000). On harmonic curvatures of a Frenet curve. , 15 - 23.
Chicago ARSLAN K.,ÇELİK Y.,HACISALİHOĞLU H. H. On harmonic curvatures of a Frenet curve. (2000): 15 - 23.
MLA ARSLAN K.,ÇELİK Y.,HACISALİHOĞLU H. H. On harmonic curvatures of a Frenet curve. , 2000, ss.15 - 23.
AMA ARSLAN K,ÇELİK Y,HACISALİHOĞLU H On harmonic curvatures of a Frenet curve. . 2000; 15 - 23.
Vancouver ARSLAN K,ÇELİK Y,HACISALİHOĞLU H On harmonic curvatures of a Frenet curve. . 2000; 15 - 23.
IEEE ARSLAN K,ÇELİK Y,HACISALİHOĞLU H "On harmonic curvatures of a Frenet curve." , ss.15 - 23, 2000.
ISNAD ARSLAN, K. vd. "On harmonic curvatures of a Frenet curve". (2000), 15-23.
APA ARSLAN K, ÇELİK Y, HACISALİHOĞLU H (2000). On harmonic curvatures of a Frenet curve. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 49(1-2), 15 - 23.
Chicago ARSLAN K.,ÇELİK Y.,HACISALİHOĞLU H. H. On harmonic curvatures of a Frenet curve. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 49, no.1-2 (2000): 15 - 23.
MLA ARSLAN K.,ÇELİK Y.,HACISALİHOĞLU H. H. On harmonic curvatures of a Frenet curve. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.49, no.1-2, 2000, ss.15 - 23.
AMA ARSLAN K,ÇELİK Y,HACISALİHOĞLU H On harmonic curvatures of a Frenet curve. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2000; 49(1-2): 15 - 23.
Vancouver ARSLAN K,ÇELİK Y,HACISALİHOĞLU H On harmonic curvatures of a Frenet curve. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2000; 49(1-2): 15 - 23.
IEEE ARSLAN K,ÇELİK Y,HACISALİHOĞLU H "On harmonic curvatures of a Frenet curve." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 49, ss.15 - 23, 2000.
ISNAD ARSLAN, K. vd. "On harmonic curvatures of a Frenet curve". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 49/1-2 (2000), 15-23.