Gauss equation
= Gauss equation
{c}
{wiki=Gauss–Codazzi_equations}
For a Euclidean embedded submanifold,
$$
\langle R(X,Y)Z,W\rangle
=\langle A(X,W),A(Y,Z)\rangle-\langle A(X,Z),A(Y,W)\rangle.
$$
It expresses intrinsic curvature in terms of the <second fundamental form>.