On Involutes of Order k of a Space-like Curve in Minkowski 4-space IE
Bir x eğrisinin birinci teğetlerinin dik yörüngelerine eğrinin involütleri adı verilir. Bu çalışmada, IE41.
IE4Minkowski 4-uzayında bir Space-like Eğrinin k'yinci Mertebeden İnvolütleri Üzerine
The orthogonal trajectories of the first tangents of a curve x are called the involutes of x. In this study, we give a characterization of involutes of order k of a space-like curve x with time-like principal normal in Minkowski 4-space IE41.
___
- Blazenka, D. And Zeljka M.S.,1999. Involutes and evolutes in n-dimensional simply isotropic space. Journal of Information and Organizational Sciences, 2(3), 71-79.
- Gluck, H., 1966. Higher curvatures of curves in Euclidean space. American Mathematical Monthly, 73, 699-704.
- Kılıc, B., Arslan, K. and Öztürk, G., 2008. Tangentially cubic curves in Euclidean spaces. Differential Geometry- Dynamical Systems, 10, 186-196.
- Klein, F. and Lie, S., 1871. Uber diejenigen ebenenen kurven welche durch eingeschlossenes system von einfach unendlich vielen vartauschbaren linearen transformationen in sich übergehen. Mathematische Annalen, 4, 50-84.
- Monterde, J., 2007. Curves with constant curvature ratios. Bulletin of Mexican Mathematic Society, Ser. 3A, (1), 177-186.
- O'Neill, B., 1983. Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York.
- Öztürk, G., Arslan, K. and Hacisalihoglu, H. H., 2008. A characterization of ccr-curves in m IR . Proccedings of Estonian Academy Science, 57(4), 217-224.
- Öztürk, G., Arslan, K. and Bulca, B., 2016. A characterization of involutes and evolutes of a given curve in n IE . arxiv.org.
- Salkowski E., 1909. Zur transformation von raumkurven. Mathematische Annalen, 66(4), 517-557.
- Turgut, M., Ali, A.T., and Lopez-Bonilla, J. L., 2010. Timelike involutes of a space-like helix in Minkowski spacetime. Apeiron, 17(1), 28-41.
- Walfare, J., 1995. Curves and surfaces in Minkowski space. PhD thesis, K.U. Leuven, Faculty of Science,Leuven.
- Yılmaz, S. and Turgut, M., 2008. On the differential geometry of the curves in Minkowski space-time I. International Journal of Contemporary Mathematical Science, 3(27), 1343-1349.