Normal connection
= Normal connection
{title2=$\nabla^\perp_X\xi=(D_X\xi)^\perp$}
The ambient <Levi-Civita connection> induces this <metric connection> on the <normal bundle> of an <embedded submanifold>. Its tangential counterpart appears in the <Weingarten formula>. Projecting the derivative preserves the <connection on a vector bundle> Leibniz rule and the fiber <inner product>.