I tryed resolve the follow problem, but I get not. Someone can help me ?
Let be $N^3$ a smooth Riemannian manifolds and let be $\Sigma^2$ a closed and embedded minimal surface of $ N $. Show that
$$K_\Sigma = K_N -2Ric^N - | A_\Sigma | ^ 2. $$
Where $ K $ is Gauss curvature and $A_\Sigma$ is second fundamental form of $\Sigma$. Hint: Took the trace in Gauss equation twice and useding that $\Sigma$ is minimal.