As the shell becomes thicker, the contribution of Gauss curvature tensor in terms of energy is no more negligible as compared to that of the first two tensors used in classical thin shells.

Finally as previous, the Gauss curvature tensor is expressed as

The mathematical root of our paper is the pioneering work of mathematician Richard Hamilton on the

Gauss curvature flow.

The Gauss curvature of the affine translation surface given by (3.

The Gauss curvature K of the generalized Scherk surface (3.

3) and the Gauss equation that the Gauss curvature K of M is given by

In this case, M is a Lorentz surface of constant Gauss curvature and [alpha][delta] = [beta][gamma] = 0 from (3.

When n = 2, the Gauss-Kronecker curvature is simply called the

Gauss curvature, which is intrinsic due to well-known Gauss' theorema egregium.

On the other hand, the

Gauss curvature K, the mean curvature H are given by

Next, looking at the local isometric embedding of surfaces in R3, they discuss metrics with

Gauss curvature that is everywhere positive, negative, nonnegative, nonpositive, as well as the case of the mixed sign.

3] gives us that the

Gauss curvature is the product of the principal curvatures.

For this purpose, we restrict to the family of rotation surfaces because the constant

Gauss curvature equation reduces into an ordinary differential equation.