Get M ,compact , an oriented minimal immersed surface of $S^3$. In the case where M is a minimal surface, the Gauss equation, gives us a relation between the norm of the shape operator, $||A||^2$, and the Gauss curvature of the surface, K. Namely,
$K=1- \frac{||A||^2}{2}$
Where $||A||$ is the norm of the second fundamental form.
I tried use the Gauss equation for the curvature tensor to show it, but it isn't clear for me. Maybe its necessary use other equation, any suggestion?