Classification of minimal Lorentzian surfaces in S₂⁴ (1) with constant Gaussian and normal curvatures

In this paper we consider Lorentzian surfaces in the 4-dimensional pseudo- Riemannian sphere S₂⁴ (1) with index 2 and curvature one. We obtain the complete Classification of minimal Lorentzian surfaces S₂⁴ (1) whose Gaussian and normal curvatures are constants. We conclude that such surfaces have the Gaussian curvature 1/3 and the absolute value of normal curvature 2/3. We also give some explicit examples.