Surfaces with $ H^{2} $= K along a given curve

In the present paper, we handle the problem of construction of surfaces with a given curve whose squared mean curvature is equal to the Gaussian curvature, that is H^{2} = K, along the given curve. We express surfaces parametrically possessing the given curve and obtain conditions for the coefficient functions to satisfy H^{2} = K along the curve. The theory is validated by illustrative examples.