##### Title: On the Equiform Differential Geometry of AW(k)-Type Curves in Pseudo-Galilean 3-Space

##### Pages: 1-15

##### Cite as:

M. Khalifa Saad, H. S. Abdel-Aziz, On the Equiform Differential Geometry of AW(k)-Type Curves in Pseudo-Galilean 3-Space, Int. J. Anal. Appl., 18 (1) (2020), 1-15.#### Abstract

The aim of this paper is to study AW(k)-type (1 ≤ k ≤ 3) curves according to the equiform differential geometry of the pseudo-Galilean space G1 3. We give some geometric properties of AW(k) and weak AW(k)-type curves. Moreover, we give some relations between the equiform curvatures of these curves. Finally, examples of some special curves are given and plotted to support our main results.

##### Full Text: PDF

#### References

- I. Yaglom, A simple non-Euclidean geometry and its physical basis, Springer-Verlag, in New York, 1979.
- B. J. Pavkovic, Equiform geometry of curves in the isotropic spaces I 1 3 and I 2 3 , Rad JAZU, 1986, 39-44.
- B. J. Pavkovic and I. Kamenarovic, The equiform differential geometry of curves in the Galilean space G3, Glasnik Mat. 22 (42) (1987), 449-457.
- K. Arslan and A. West, Product submanifolds with pointwise 3-planar normal sections, Glasgow Math. J. 37 (1) (1995), 73-81.
- K. Arslan and C. Ozgur, Curves and surfaces of AW(k) -type, Geometry and topology of submanifolds IX, World Scientific, 1999, 21-26.
- M. Kulahci, M. Bektas and M. Ergut, On harmonic curvatures of null curves of the AW(k)-type in Lorentzian space, Z. Naturforsch. A, 63 (5-6) (2008), 248-252.
- M. Kulahci and M. Ergut, Bertrand curves of AW(k)-type in Lorentzian space, Nonlinear Anal., Theory Methods Appl. 70 (2009), 1725-1731.
- M. Kulahci, A.O. Ogrenmis and M. Ergut, New characterizations of curves in the Galilean space G3, Int. J. Phys. Math. Sci. 1 (2010), 49-57.
- C. Ozgur and F. Gezgin, On some curves of AW(k)-type, Differ. Geom. Dyn. Syst. 7 (2005), 74-80.
- D. W. Yoon, General Helices of AW(k)-Type in the Lie Group, J. Appl. Math. 2012 (2012), Article ID 535123.
- Z. Erjavec and B. Divjak, The equiform differential geometry of curves in the pseudo-Galilean space, Math. Commun. 13 (2008), 321-332.
- Z. Erjavec, On generalization of helices in the Galilean and the pseudo-Galilean space, J. Math. Res. 6 (3) (2014), 39-50.
- B. Divjak, The general solution of the Frenet’s system of differential equations for curves in the pseudo-Galilean space G1 3 , Math. Commun. 2 (1997), 143-147.
- B. Divjak, Geometrija pseudogalilejevih prostora, Ph. D. thesis, University of Zagreb, 1997.
- B. Divjak, Curves in pseudo-Galilean geometry, Ann. Univ. Sci. Budapest. Sect. Math. 41 (1998), 117-128.