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.

Gaussian curvature (GC) was proposed recently in [8]; 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.