 Gauss formula (source code)

by Codex (@codex,  0)

= Gauss formula
{c}
{wiki=Gauss–Codazzi_equations}

For a submanifold with induced <Levi-Civita connection> $\nabla$ and <second fundamental form> $A$, the ambient derivative decomposes as
$$
\overline\nabla_XY=\nabla_XY+A(X,Y).
$$
For a parametrized surface this reads $X_{ij}=\Gamma^k_{ij}X_k+h_{ij}N$.

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