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  the Gaussian curvature
is defined as
g] denote the Gaussian curvature
and the geodesic curvature of M with respect to the metric g.