We modify the deformation method from [9] in order to construct further examples of Kobayashi hyperbolic surfaces in P of any even degree d ≥ 8. Given a hypersurface Xd = f ∗ d (0) in P n of degree d, we say that a (very) general small deformation of Xd is hyperbolic if for any (very) general degree d hypersurface X∞ = g ∗ d(0) and for all sufficiently small ε ∈ C \ {0} (depending on X∞) the hy...

Plasmonic nanostructures have been extensively used to manipulate the spontaneous light emission rate of molecules and their radiative efficiency. Because molecules near a metallic surface experience a different environment than in free space, their spontaneous radiative emission rate is generally enhanced. Such enhancement, measured by means of the Purcell factor, arises as a consequence of th...

We prove a partial generalization of Bonahon’s tameness result to surfaces inside irreducible 3–manifolds with hyperbolic fundamental group. Bonahon’s result states that geometrically infinite ends of freely indecomposable hyperbolic 3–manifolds are simply degenerate. It is easy to see that a geometrically infinite end gives rise to a sequence of curves on the corresponding surface whose geodes...

The present paper focuses on numerical study for an inclined magneto-hydrodynamic effect on free convection flow of a tangent hyperbolic nanofluid embedded with Carbon nanotubes (CNTs) over a stretching surface taking velocity and thermal slip into account. Two types of nanoparticles are considered for the study; they are single and multi-walled nanotubes. The presentation of single-parameter g...

The perception of a three-dimensional (3-D) surface shape can be inferred from a 2-D image of two intersecting curves. Three experiments are reported in which we examined a possible method for determining the surface shape as a function of the geometry at the point of intersection. The method involves a two-step process in which the tangents to the two curves determine a skewed Cartesian coordi...

Ruled surface design and its applications are widely used in CAGD(Computer Aid Geometric Design) and industrial areas. In this paper, the hyperbolic paraboloid is a particular ruled surface, which is drawn by using the dual De Casteljau algorithm [15]. The characteristics of the hyperbolic paraboloid are analysed in order to match the requirement of the dual De Casteljau algorithm. A new method...

Let X be a closed oriented Riemann surface of genus ≥ 2 of constant negative curvature −1. A surface containing a disk of maximal radius is an optimal surface. This paper gives exact formulae for the number of optimal surfaces of genus ≥ 4 up to orientation-preserving isometry. We show that the automorphism group of such a surface is always cyclic of order 1, 2, 3 or 6. We also describe a combi...

How well do observers perceive the local shape of an object from its shaded image? This problem was addressed by first deriving a potential representation of local solid shape. The descriptor of local shape, called shape characteristic, provides a viewpoint-independent continuum between hyperbolic (saddle-shaped) and elliptic (egg-shaped) points. The ability of human observers to make categoric...

A constant angle surface in Minkowski space is a spacelike surface whose unit normal vector field makes a constant hyperbolic angle with a fixed timelike vector. In this work we study and classify these surfaces. In particular, we show that they are flat. Next we prove that a tangent developable surface (resp. cylinder, cone) is a constant angle surface if and only if the generating curve is a ...