Osculating Spheres of a Semi Real Quaternionic Curve in E_2^4

Abstract

In this study, we define the osculating spheres of a semi real quaternionic curve in Semi Euclidean spaces $\mathbb{E}_{1}^{3}~$and $\mathbb{E}_{2}^{4}$. We gave the equation of the osculating
spheres with respect to Frenet frames $\left\{ \mathbf{t}_{0},\mathbf{n}%
_{1_{0}},\mathbf{n}_{2_{0}}\right\} ~$and $\left\{ \mathbf{T}_{0},\mathbf{N}%_{\mathbf{1}_{0}},\mathbf{N}_{\mathbf{2}_{0}},\mathbf{N}_{\mathbf{3}%
_{0}}\right\} $.