Radius of Curvature: Formula & Name

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I am working on a paper that provides the following formula for computing radius of curvature at a point on a surface.

\frac{1}{\rho_c}=\frac{\partial G/\partial S}{2\sqrt{E}G}

where E,G are first fundamental coefficients and S is the arc length parameter.

Can anyone please tell me the name of the curvature the above mentioned formula computes.
 
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