In this paper, we discuss the isometric embedding problem in hyperbolic space with nonnegative extrinsic curvature. We prove a priori bounds for the trace of the second fundamental form H and extend the result to ndimensions. We also obtain an estimate for the gradient of the smaller principal curvature in 2 dimensions.

This paper describes a new surface normal smoothing process which can be used in conjunction with shape-fromshading. Rather than directly smoothing the surface normal vectors, we exert control over their directions by smoothing the field of principal curvature vectors. To do this we develop a topography sensitive smoothing process which overcomes the problems of singularities in the field of pr...

In this paper are studied the nets of principal curvature lines on surfaces embedded in Euclidean 3−space near their end points, at which the surfaces tend to infinity. This is a natural complement and extension to smooth surfaces of the work of Garcia and Sotomayor (1996), devoted to the study of principal curvature nets which are structurally stable –do not change topologically– under small p...

We have learned that the two principal curvatures (and vectors) determine the local shape of a point on a surface. One characterizes the rate of maximum bending of the surface and the tangent direction in which it occurs, while the other characterizes the rate and tangent direction of minimum bending. The rate of surface bending along any tangent direction at the same point is determined by the...

In this paper is studied the relationship between quadratic tangencies of principal lines with the boundary of a surface and the Darbouxian umbilics of a smooth boundaryless surface which approximates it through the process of thickening and smoothing defined here.

We investigate one-parameter family of transformation on superfields of super principal chiral model and obtain different zero-curvature representations of the model. The parametric transformation is related to the super Riccati equations and an infinite set of local and non-local conservation laws is derived. A Lax representation of the model is presented which gives rise to a superspace monod...

Free Ca2+ changes the curvature of epididymal rat sperm flagella in demembranated sperm models. The radius of curvature of the flagellar midpiece region was measured and found to be a continuous function of the free Ca2+ concentration. Below 10(-7) M free Ca2+, the sperm flagella assumed a pronounced curvature in the same direction as the sperm head. The curvature reversed direction at 2.5 x 10...

The muscle bundles of the diaphragm form a curved sheet that extends from the chest wall to the central tendon. Each muscle bundle exerts a force in the direction of its curvature; the magnitude of this force is proportional to the curvature of the bundle. The contribution of this force to transdiaphragmatic pressure is maximal if the direction of bundle curvature is orthogonal to the surface a...

We develop the local theory of surfaces immersed in the pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo-Galilean space is provided. We describe surfaces of revolution of constant curvature. We introduce special local coordinates for surfaces of...

We establish extensions of the Crofton formula and, under some restrictions, of the principal kinematic formula of integral geometry from curvature measures to generalized curvature measures of convex bodies. We also treat versions for nite unions of convex bodies. As a consequence, we get a new intuitive interpretation of the area measures of Aleksandrov and Fenchel{ Jessen. The subject of thi...