= A conformal Gauss map does not imply a minimal surface
{title2=$A^2=\mu I$}
For a <minimal surface>, the <shape operator> has eigenvalues $k,-k$, so $\langle dN(v),dN(w)\rangle=k^2\langle v,w\rangle$. Conversely this metric identity only implies that the two principal curvatures have equal squares. A sphere has equal nonzero principal curvatures and satisfies the identity while having nonzero <mean curvature>. The distinction is between opposite and equal signs, not equality of magnitudes.
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