Looks like related but not duplicate threads to me.

@simonnpro Frame is a plane related to the geometry of a surface at a point.

Gaussian and Mean values of curvature are simple scalar metrics of the curvature of a plane at a point.

The curvature of a surface at a point usually varies depending on which direction the curvature is measured.

The usual method for completely describing the curvature of a surface is the principal curvatures and a direction. As long as the curvature is continuous at a point there will be one direction where the curvature is the maximum (largest). In the direction perpendicular the curvature will be the minimum (smallest). These are the principal curvatures. Note that largest and smallest include signs. So if the two curvatures are 2 and -5 then 2 is the largest and -5 is the smallest. If the two curvatures are -3 and -6 then -3 is the largest and -6 is the smallest. Also note that some Rhino commands for principal curvatures, minimum and maximum curvatures only show the absolute values which can be confusing.

Mean curvature is the average value of the two principal curvatures.

Gaussian curvature is the product of the principal curvatures. A surface which is concave or convex will have positive Gaussian curvature. A surface which is developable (one of the principal curvatures is zero) will have zero Gaussian curvature. A surface which is anticlastic or saddle shaped will have negative Gaussian curvature.