We show the existence of several new families of non-compact constant mean curvature surfaces: (i) singly-punctured surfaces of arbitrary genus g ≥ 1, (ii) doubly-punctured tori, and (iii) doubly periodic surfaces with Delaunay ends.

Bäcklund transformations for smooth and “space discrete” Hashimoto surfaces are discussed and a geometric interpretation is given. It is shown that the complex curvature of a discrete space curve evolves with the discrete nonlinear Schrödinger equation (NLSE) of Ablowitz and Ladik, when the curve evolves with the Hashimoto or smoke ring flow. A doubly discrete Hashimoto flow is derived and it i...

Curvature discrimination of hand-sized doubly curved surfaces by means of static touch was investigated. Stimuli consisted of hyperbolical, cylindrical, elliptical and spherical surfaces of various curvatures. In the first experiment subjects had to discriminate the curvature along a specified orientation (the discrimination orientation) of a doubly curved surface from a flat surface. The curva...

Curvature discrimination of hand-sized doubly curved surfaces by means of static touch was investigated. Stimuli consisted of hyperbolical, cylindrical, elliptical and spherical surfaces of various curvatures. In the ®rst experiment subjects had to discriminate the curvature along a speci®ed orientation (the discrimination orientation) of a doubly curved surface from a ̄at surface. The curvatur...

In the present paper, we form a sharp inequality for doubly warped product submanifold of Riemannian manifold nearly quasi-constant curvature.

Non-linear special relativity (or doubly special relativity) is a simple framework for encoding properties of flat quantum space-time. In this paper we show how this formalism may be generalized to incorporate curvature (leading to what might be called “doubly general relativity”). We first propose a dual to nonlinear realizations of relativity in momentum space, and show that for such a dual t...

Non-linear special relativity (or doubly special relativity) is a simple framework for encoding properties of flat quantum space-time. In this paper we show how this formalism may be generalized to incorporate curvature (leading to what might be called “doubly general relativity”). We first propose a dual to non-linear realizations of relativity in momentum space, and show that for such a dual ...