JOURNAL BROWSE
Search
Advanced SearchSearch Tips
BERTRAND CURVES IN NON-FLAT 3-DIMENSIONAL (RIEMANNIAN OR LORENTZIAN) SPACE FORMS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
BERTRAND CURVES IN NON-FLAT 3-DIMENSIONAL (RIEMANNIAN OR LORENTZIAN) SPACE FORMS
Lucas, Pascual; Ortega-Yagues, Jose Antonio;
  PDF(new window)
 Abstract
Let denote the 3-dimensional space form of index $q
 Keywords
Bertrand curve;general helix;null curve;non-null curve;
 Language
English
 Cited by
1.
Curves in Three Dimensional Riemannian Space Forms, Results in Mathematics, 2014, 66, 3-4, 469  crossref(new windwow)
2.
Mannheim Curves in Nonflat 3-Dimensional Space Forms, Advances in Mathematical Physics, 2015, 2015, 1  crossref(new windwow)
 References
1.
Y. A. Aminov, Differential Geometry and Topology of Curves, Gordon and Breach Science Publishers, Singapore, 2000.

2.
M. Barros, General helices and a theorem of Lancret, Proc. Amer. Math. Soc. 125 (1997), no. 5, 1503-1509. crossref(new window)

3.
M. Barros, A. Ferrandez, P. Lucas, and M. A. Merono, Solutions of the Betchov-Da Rios soliton equation: A Lorentzian approach, J. Geom. Phys. 31 (1999), no. 2-3, 217-228. crossref(new window)

4.
M. Barros, A. Ferrandez, P. Lucas, and M. A. Merono, General helices in the 3-dimensional Lorentzian space forms, Rocky Mountain J. Math. 31 (2001), no. 2, 373-388. crossref(new window)

5.
J. Bertrand, Memoire sur la theorie des courbes e double courbure, Comptes Rendus 36 (1850); Journal de Mathematiques Pures et Appliquees 15 (1850), 332-350.

6.
G. S. Birman and K. Nomizu, Trigonometry in Lorentzian geometry, Amer. Math. Monthly 91 (1984), no. 9, 543-549. crossref(new window)

7.
G. S. Birman and K. Nomizu, Gauss-Bonnet theorem for 2-dimensional spacetimes, Michigan Math. J. 31 (1984), no. 1, 77-81. crossref(new window)

8.
Y.-M. Cheng and C.-C. Lin, On the generalized Bertrand curves in Euclidean N-spaces, Note Mat. 29 (2009), no. 2, 33-39.

9.
K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers, Dordrecht, 1996.

10.
N. Ekmekci and K. Ilarslan, On Bertrand curves and their characterization, Differ. Geom. Dyn. Syst. 3 (2001), no. 2, 17-24.

11.
S. Ersoy and M. Tosun, Timelike Bertrand Curves in Semi-Euclidean Space, arXiv:1003.1220v1[math.DG]

12.
A. Ferrandez, A. Gimenez, and P. Lucas, Null helices in Lorentzian space forms, Internat. J. Modern Phys. A 16 (2001), no. 30, 4845-4863. crossref(new window)

13.
A. Gorgulu and E. Ozdamar, A generalization of the Bertrand curves as general inclined curves in En, Comm. Fac. Sci. Univ. Ankara Ser. A1 Math. Statist. 35 (1986), no. 1-2, 53-60.

14.
A. Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapter 3.5, Clothoids, pages 64-66. CRC Press, Boca Raton, FL, 2nd edition, 1997.

15.
G. Harary and A. Tal, 3D Euler spirals for 3D curve completion, In Proceedings of the 2010 Annual Symposium on Computational Geometry SoCG'10 (2010), 393-402. ISBN:978-1-4503-0016-2.

16.
M. Kulahc and M. Ergut, Bertrand curves of AW(k)-type in Lorentzian space, Nonlinear Anal. 70 (2009), no. 4, 1725-1731. crossref(new window)

17.
H. F. Lai, Weakened Bertrand curves, Tohoku Math. J. 19 (1967), 141-155. crossref(new window)

18.
H. Matsuda and S. Yorozu, Notes on Bertrand curves, Yokohama Math. J. 50 (2003), no. 1-2, 41-58.

19.
E. Nessovic, M. Petrovic-Torgasev, and L. Verstraelen, Curves in Lorentzian spaces, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 8 (2005), no. 3, 685-696.

20.
H. B. Oztekin, Weakened Bertrand curves in the Galilean space $G_3$, J. Adv. Math. Stud. 2 (2009), no. 2, 69-76.

21.
L. R. Pears, Bertrand curves in Riemannian space, J. London Math. Soc. (1935) s1-10 (3), 180-183.

22.
J. C. Saint-Venant, Memoire sur les lignes courbes non planes, Journal d'Ecole Polytechnique 30 (1845), 1-76.

23.
M. Y. Yilmaz and M. Bektas, General properties of Bertrand curves in Riemann-Otsuki space, Nonlinear Anal. 69 (2008), no. 10, 3225-3231. crossref(new window)