Abstract. The magnetic moment of an electron gas on the surface of constant negative curvature is investigated. It is shown that the surface curvature leads to the appearance of the region of the monotonic dependence M(B) at low magnetic fields. At high magnetic fields, the dependence of the magnetic moment on a magnetic field is the oscillating one. The effect of the surface curvature is to in...

We examined the effects of vertical-disparity gradients on apparent depth curvature of textured surfaces. In Experiment 1, vertical disparities induced expected curvatures when the surface had a horizontal disparity of < +/-40.34'. A central row of elements, lacking vertical disparities, ceased to have the same apparent curvature as the surface when the horizontal disparity between row and surf...

This paper explores the representation of the human face by features based on shape and curvature of the face surface Curvature captures many features necessary to accurately describe the face such as the shape of the forehead jaw line and cheeks which are not easily detected from standard intensity images Moreover the value of curvature at a point on the surface is also viewpoint invariant Unt...

The fact that the Darboux frame is rotation–minimizing along lines of curvature of a smooth surface is invoked to construct rational surface patches whose boundary curves are lines of curvature. For given patch corner points and associated frames defining the surface normals and principal directions, the patch boundaries are constructed as quintic RRMF curves, i.e., spatial Pythagorean–hodograp...

N. V. Efimov [Efi64] proved that there is no complete, smooth surface in R with uniformly negative curvature. We extend this to isometric immersions in a 3-manifold with pinched curvature: if M has sectional curvature between two constants K2 and K3, then there exists K1 < min(K2, 0) such that M contains no smooth, complete immersed surface with curvature below K1. Optimal values of K1 are dete...

This paper gives a construction to complete, at extraordinary points, an otherwise bi-cubic spline surface – so that the resulting surface is curvature continuous everywhere. To fill the n-sided gap in the bi-cubic surface, a cap is constructed from n spline patches, each consisting of 2× 2 pieces of polynomial degree bi-5. Particular care is taken to continue the curvature distribution from th...

Acoustic wave propagation in elastic media is characterized by the slowness surface. The slowness surface consists of three sheets associated with three modes of wave propagation and the two outer sheets can have zero-curvature locally. It is shown that the outmost sheet can admit extraordinary zero-curvature and the slowness curve can appear as a straight line locally. Using the perturbation m...