An approach for vectorial moments in Euclidean 3-space

In this paper, we investigate the vectorial moments of B\"{a}cklund transformations of a space curve in $\mathbb{E}^{3}$. Firstly, it is obtained the vectorial moments which named $\alpha _{\mathcal{G}}$ dual curve, $\beta _{\mathcal{G}}$ dual curve, and $\gamma _{\mathcal{G}}$ dual curve of B\"{a}cklund transformations. Then we give\ the Euler elastic bending energies of these curves. Finally, we provide some examples of $\alpha _{\mathcal{G}}$ dual, $\beta _{\mathcal{G}}$ dual, and$\gamma_{\mathcal{G}}$ dual, and their Euler elastic bending energies. KCI Citation Count: 0