Get the classical Gauss's equation $\langle R_{x,y}Z,W \rangle = \langle X,W \rangle \langle Y,Z \rangle - \langle X,Z \rangle \langle Y,W \rangle - \langle A(x), Z \rangle \langle A(y), W \rangle + \langle A(x), W \rangle \langle A(y),Z \rangle $
$X,Y,Z,W \in TM$
Since $\phi:M^n \implies S^{n+1}$ is minimal immersion and A the second fundamental form
I want calculate the trace twice to show $K=1-\frac{1}{n(n-1)}||A||^2$, K is the scalar curvature.
any ideia?
Thank you advance!