therefore it is the space of constant positive curvature, where q is the

Gaussian curvature of the three-dimensional reference space.

The Monge-Ampere equation is a fully nonlinear degenerate elliptic equation arising in several problems in the areas of analysis and geometry, such as the prescribed

Gaussian curvature equation, affine geometry, and optimal transportation, says Figalli.

the integral of

Gaussian curvature with respect to the geodesic triangle) is a measure of traversability of [DELTA].

The rulings are principal curvature lines with vanishing normal curvature and the

Gaussian curvature vanishes at all surface points.

The

Gaussian curvature K and the normal curvature [K.

The sine-Gordon equation which arises in the study of differential geometry of surfaces with

Gaussian curvature has wide applications in the propagation of fluxon in Josephson junctions (Perring and Skyrme 1962 Whitham 1999 Sirendaoreji and Jiong 2002 Fu et al.

He concluded that one can study the shell with holes of positive or zero

Gaussian Curvature, with a hole limited to a soft environment (with no angle like a circle) which bending is enough soft and flexible, as a shallow shell.

Then K : M [right arrow] R, K(P) = det S(P) function is called the

Gaussian curvature function of M.

This is actually the negative of the usual

Gaussian curvature defined in text books.

They use a new algorithm to approximate the mean and

Gaussian curvature of a mesh, which are then combined in a nonlinear way.

In Section 3E of [3] the

Gaussian curvature is defined as

g] denote the

Gaussian curvature and the geodesic curvature of M with respect to the metric g.