Turkish Journal of Mathematics
Abstract
The pseudo spherical indicatrix of a curve in Minkowski $3$-space emerges as three types: the pseudo spherical tangent indicatrix, principal normal indicatrix, and binormal indicatrix of the curve. The pseudo spherical tangent, principal normal, and binormal indicatrix of a regular curve may be positioned on De Sitter $2$-space (pseudo sphere), pseudo hyperbolic 2-space, and two-dimensional null cone in terms of causal character of the curve. In this paper, we separately derive Euler-Lagrange equations of all pseudo spherical indicatrix elastic curves in terms of the causal character of a curve in Minkowski $3$-space. Then we give some results of solutions of these equations.
DOI
10.3906/mat-1801-44
Keywords
Elastic curve, Euler-Lagrange equation, pseudo spherical indicatrix
First Page
3123
Last Page
3132
Recommended Citation
YÜCESAN, A, TÜKEL, G. Ö, & TURHAN, T (2018). Curves whose pseudo spherical indicatrices are elastic. Turkish Journal of Mathematics 42 (6): 3123-3132. https://doi.org/10.3906/mat-1801-44
