On non-parametric surfaces in three dimensional spheres

On Hamiltonian Stationary Lagrangian Spheres in Non-einstein Kähler Surfaces

Hamiltonian stationary Lagrangian spheres in Kähler-Einstein surfaces are minimal. We prove that in the family of non-Einstein Kähler surfaces given by the product Σ1×Σ2 of two complete orientable Riemannian surfaces of different constant Gauss curvatures, there is only a (non minimal) Hamiltonian stationary Lagrangian sphere. This example is defined when the surfaces Σ1 and Σ2 are spheres.

Non-Degenerate Spheres in Three Dimensions

Let P be a set of n points in R, and k ≤ n an integer. A sphere σ is k-rich with respect to P if |σ ∩ P | ≥ k, and is η-nondegenerate, for a fixed fraction 0 < η < 1, if no circle γ ⊂ σ contains more than η|σ ∩ P | points of P . We improve the previous bound given in [1] on the number of k-rich η-nondegenerate spheres in 3space with respect to any set of n points inR, from O(n/k+n/k), which hol...

Computational study of three dimensional potential energy surfaces in intermolecular hydrogen bonding of cis-urocanic acid

On Bézier surfaces in three-dimensional Minkowski space

0. Introduction A Bézier surface is defined using mathematical spline functions whereby the resulting surface has a compact analytic description. This enables such surfaces to be easily manipulated, and they also have greater continuity properties. Bézier curves and surfaces are commonly used in computer-aided design [1,2], image processing [3,4], and finite elementmodeling (e.g. [5–7]). Many o...

Smooth surfaces in three-dimensional Euclidean space

are locally described by classical differential geometry. In case some spatial direction (e.g., the direction of gravity in the natural landscape or the viewing direction in visual space) assumes a special role, this formalism has to be replaced by the special theory of “topographic surfaces’’ and one speaks of “surface relief ’’ (Liebmann, 1902/1927). Examples include topographic relief and— i...