On the involute and evolute curves of the timelike curve in Minkowski 3-space

• Autorzy: Bukcu B. , Karacan K.
• Języki publikacji: EN

Abstrakty

EN

In this study, we have generalized the involute and evolute curves of the timelike curve in Minkowski 3-Space. Firstly, we have shown that, the length between the timelike curve alpha and the spacelike curve beta is constant. Furthermore, the Frenet-Serret frame of the involute curve beta has been found as dependent on curvatures of the curve alpha. We have determined the involute curve beta is planar in which conditions. Secondly, we have found transformation matrix between the evolute curve beta and the curve alpha. Finally, we have computed the curvatures of the evolute curve beta.

Słowa kluczowe

EN

timelike curve; involutes; evolutes; Minkowski space

PL

krzywa typu czasowego; ewoluta; ewolwenta; przestrzeń Minkowskiego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 3
• Strony: 721--732
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Bukcu B.

autor

Karacan K.

• Gazi Osman Pasa University Faculty of Sciences and Letters Department of Mathematics Tokat-Turkey,

Bibliografia

• [1] H. H. Hacisalihoglu, Solutions of the differential geometry problems, Ankara University, Faculty of Science, 1995.
• [2] M. Petrovic and E. Sucurovic, Some characterizations of the spacelike, the timelike and the null curves on the pseudohyperbolic space H2/0 in E3/1 , Kragujevac J. Math. 22 (2000), 71-82.
• [3] A. Sabuncuoglu, Differential Geometry, Nobel Yayin Dagitim, Ankara, 2004.