It is the normal curvature of an immersed surface along a principal direction, i.e. along a direction in which it assumes an extremal value. They are usually denoted by $\kappa_1$ and $\kappa_2$. Their product is the Gaussian curvature.
They can be computed as the eigenvalues of the shape operator, that is, the second fundamental form with raised index.
In matrix notation if
$$ \mathcal{F}_{1}=\left(\begin{array}{cc} E & F \\ F & G \end{array}\right) \quad \text { and } \quad \mathcal{F}_{2}=\left(\begin{array}{cc} L & M \\ M & N \end{array}\right) $$then $\kappa_1$ and $\kappa_2$ are the eigenvalues of $\mathcal{F}_{1}^{-1} \mathcal{F}_{2}$.
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Author of the notes: Antonio J. Pan-Collantes
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