TY  - JOUR
T1  - Euclidean Curves with Incompressible Canonical Vector Field
AU  - Arslan, Kadri
AU  - Aydın, Yılmaz
AU  - Demirbaş, Eray
AU  - Yazla, Aziz
PY  - 2018
DA  - December
Y2  - 2019
JF  - Adıyaman University Journal of Science
JO  - ADYU J SCI
PB  - Adıyaman University
WT  - DergiPark
SN  - 2147-1630
SP  - 70
EP  - 82
VL  - 8
IS  - 2
LA  - en
AB  - Inthe present study we consider Euclidean curves with incompressible canonicalvector fields. We investigate such curves in terms of their curvaturefunctions. Recently, B.Y. Chen gave classification of plane curves withincompressible canonical vector fields. For higher dimensional case we gave acomplete classification of Euclidean space curves with incompressible canonicalvector fields. Further we obtain some results of the Euclidean curves with incompressiblecanonical vector fields in -dimensional Euclidean space E4.
KW  - Generalized helix
KW  - Salkowski curve
KW  - Regular curve
KW  - Canonical vector field
CR  - [1] A. T. Ali, Spacelike Salkowski and anti-Salkowski curves with timelike principal normal in Minkowski 3-space, Mathematica Aeterna, 1(2011), 201 - 210.
CR  - [2] B. Y. Chen, Euclidean submanifolds with incompressible canonical vector field, arXiv:1801.07196v3 [math.DG] 29 Jan 2018.
CR  - [3] J. W. Bruce, P. J. Giblin, Curves and Singularities, A Geometrical Introduction to Singularity Theory, Second edition, Cambridge University Press, Cambridge, 1992.
CR  - [4] H. Gluck, Higher curvatures of curves in Euclidean space, Am. Math. Monthly 73 (1966), 699-704.
CR  - [5] F. Klein and S. Lie, Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendlich vielen vartauschbaren linearen Transformationen in sich übergehen, Math. Ann. 4 (1871), 50-84.
CR  - [6] J. Monterde, Curves with constant curvature ratios, Bull. Mexican Math. Soc. Ser. 3A 13(1) (2007), 177-186.
CR  - [7] G. Öztürk, K. Arslan and H. H. Hacisalihoglu, A characterization of ccr-curves in R^{m}, Proc. Estonian Acad. Sci. 57(4) (2008), 217-224.
CR  - [8] G. Öztürk, S. Gürpınar and K. Arslan, A New Characterization of Curves in Euclidean 4-Space E⁴, Bull. Acad. Stiinte a Republicii Moldova Mathematica, 83(2017), 39-50.
CR  - [9] E. Salkowski, Zur transformation von raumkurven, Math. Ann. 66(4) (1909), 517-557.
UR  - https://dergipark.org.tr/en/pub/adyujsci/article/428516
L1  - https://dergipark.org.tr/en/download/article-file/620143
ER  -