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## Main Question or Discussion Point

The product of the principal curvatures of a surface in Euclidean 3 space, though defined extrinsically, is actually an intrinsic quantity, the Gauss curvature. This is the Theorem Egregium.

What about the product of the principal curvatures for higher dimensional hypersurfaces?

What about the product of the principal curvatures for higher dimensional hypersurfaces?