A NEW CHARACTERIZATION OF CURVES IN MINKOWSKI 4-SPACE E_1^4
Abstract
In this study, we attend to the curves whose position vectors are written as a
linear combination of their Serret-Frenet vectors in Minkowski 4-Space E_1^4. We characterize such curves with regard to their curvatures. Further, we get certain consequences of T-constant and N-constant types of curves in E_1^4.
Keywords
Full Text:
PDFReferences
A. A. Ali and M. Onder: Some characterization of spacelike rectifying curves in the Minkowski space-time. Global J. Sci. Front Resh. Math&Dec. Sci., 12 (2009), 57--63.
S. Buyukkutuk and G. Ozturk: Constant ratio curves according to parallel transport frame in Euclidean 4-space E4. New Trends in Mathematical Sciences, 3(4) (2015), 171--178.
S. Buyukkutuk and G. Ozturk: Constant ratio curves according to Bishop frame in Euclidean 3-space E3. Gen. Math. Notes, 28(1) (2015), 81--91.
S. Buyukkutuk, I. Kişi, V. N. Mishra, and G. Ozturk: Some characterizations of curves in Galilean 3-space G3. Facta Universitatis, Series: Mathematics and Informatics, 31(2) (2016), 503--512.
S. Buyukkutuk, I. Kişi, and G. Ozturk: A characterization of curves according to parallel transport frame in Euclidean n-space En. New Trends in Mathematical Sciences, 5(2) (2017), 61--68.
S. Buyukkutuk, I. Kişi, and G. Ozturk: A characterization of non-lightlike curves with respect to parallel transport frame in Minkowski space-time. Malaysian Journal of Mathematical Sciences, 12(2) (2018), 223--234.
B. Y. Chen: When does the position vector of a space curve always lies in its rectifying plane?, Amer. Math. Montly, 110 (2003), 147--152.
B. Y. Chen: Geometry of position functions of Riemannian submanifolds in pseudo-Euclidean space. Journal of Geo., 74 (2002), 61--77.
B. Y. Chen: Constant ratio spacelike submanifolds in pseudo Euclidean space. Houston Journal of Mathematics, 29 (2003), 281--294.
B. Y. Chen and F. Dillen: Rectifying curves as centrodes and extremal curves Bull. Inst. Math. Acedemia Sinica, 33 (2005), 77--90.
K.L. Dugal and A. Bejancu: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic, Dordrecht, 1996.
R. Ezentas and S. Turkay: Helical versus of rectifying curves in Lorentzian space. Dumlupınar Univ. Fen Bilim. Est. Dergisi, 6 (2004), 239--244.
A. Gray: Modern Dierential Geometry of Curves and Surface. CRS Press, Inc., 1993.
H. Gluck, Higher curvatures of curves in Euclidean space.
Amer. Math. Monthly, 73 (1966), 699--704.
S. Gurpınar, K. Arslan, and G. Ozturk, A characterization of constant-ratio curves in Euclidean 3-space E3. Acta Universitatis Apulensis, 44 (2015), 39--51.
K. Ilarslan, E. Nesovic, and T. M. Petrovic: Some characterization of rectifying curves in the Minkowski 3-space. Novi Sad J. Math., 32 (2003), 23--32.
K. Ilarslan and E. Nesovic: On rectifying curves as centrodes and extremal curves in the Minkowski 3-space E31. Novi. Sad. J. Math., 37 (2007), 53--64.
K. Ilarslan and E. Nesovic: Some characterization of null, peudo-null and partially null rectifying curves in Minkowski space-time. Taiwanese J. Math., 12 (2008), 1035--1044.
K. Ilarslan E. Nesovic: The rst and second kind osculating curves in Minkowski space-time. Comp. Ren. de Acad. Bul. des Sci., 62 (2009), 677--689.
I. Kisi, S. Buyukkutuk, G. Ozturk, and A. Zor, A new characterization of curves on dual unit sphere. Journal of Abstract and Computational Mathematics, 2(1) (2017), 71--76.
I. Kisi, S. Buyukkutuk, and G. Ozturk: Constant ratio timelike curves in pseudo-Galilean 3-space G13. Creative Mathematics and Informatics, 27(1) (2018), 57--62.
I. Kisi and G. Ozturk: Constant ratio curves according to Bishop frame in Minkowski 3-space E31. Facta Universitatis Ser. Math. Inform., 30(4) (2015), 527--38.
F. Klein and S. Lie: Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendlich vielen vartauschbaren linearen Transformationen in sich ubergehen. Math. Ann., 4 (1871), 50--84.
J. Monterde: Curves with constant curvature ratios. Bulletin of Mexican Mathematic Society, 13 (2007), 177--186.
B. O'Neill: Semi-Riemannian Geometry with Application to Relativity. Academic Press, 1983.
M. Ozdemir, M. Erdogdu, H. Simsek, and A.A. Ergin: Backlund transformation for spacelike curves in the Minkowski space-time. Kuwait J. Sci., 41 (2014), 63--80.
G. Ozturk, K. Arslan, and H.H. Hacisalihoglu: A characterization of ccr-curves in Rn. Proc. Estonian Acad. Sciences, 57 (2008), 217--224.
G. Ozturk, K. Arslan, and I. Kisi: Constant ratio curves in Minkowski 3-space E31. Bulletin Mathematique, 42(2) (2018), 49--60.
G. Ozturk, S. Buyukkutuk, and I. Kisi: A characterization of curves in Galilean 4-space G4. Bulletin of the Iranian Mathematical Society, 43(3) (2017), 771--780.
G. Ozturk, S. Gurpınar, and K. Arslan: A new characterization of curves in Euclidean 4-space E4. Buletinul Academiei de Stiinte a Republicii Moldova, Matematica, 83(1) (2017), 39--50.
G. Ozturk, I. Kisi, and S. Buyukkutuk: Constant ratio quaternionic curves in Euclidean spaces. Advances in Applied Clifford Algebras, 27(2) (2017), 1659--1673.
DOI: https://doi.org/10.22190/FUMI2001187K
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)