Our principal result is, howbeit, the affirmative answer to the previous question concerning the dependency of such finite amount of translation on the Gaussian curvature
of the surface at the point of interest.
Massey, Surfaces of Gaussian curvature
zero in Euclidean 3-space, Tohoku Math.
This is a static solution with the ([theta], [phi]) curved 2-surface describing a space with a positive Gaussian curvature
Killing submersions are determined by two functions on M, its Gaussian curvature
and the so-called bundle curvature (for more details, see [23, 24] and Section 2).
Soap-film models represent the equilibrium state with the lowest strain energy for shells with negative Gaussian curvature
and hanging models for shells with a positive Gaussian curvature
(GC) was proposed recently in ; it was used as a diffusion equation for noise removal, demonstrating advantages for edge and small feature preservation.
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.
A measure of total curvature (i.e., 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.sub.v] are given by
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.