In this paper, the notion of the catenary curve in the sphere and in the hyperbolic plane is
introduced. In both spaces, a catenary is defined as the shape of a hanging chain when its …

In this paper, a bilayer ultrathin (≈ 0. 153 λ) metalens is presented by exploring the
advantage of the metasurface with catenary shape and symmetry transformation. The …

Catenary optics has attracted much interest due to its unique properties in wave-front
manipulation, field enhancement, and dispersion engineering. In this paper, the applications …

We classify hypersurfaces of revolution for which the principal curvatures are proportional.
These hypersurfaces form a one-parameter family indexed by the reals. The subsequent …

It is well-known that the catenary is characterized by an extremal centroidal condition: It is
the shape of the curve whose centroid is the lowest among all curves having a prescribed …

We study the positive $ C^ 1$ function z= f (x, y) defined on the plane ${\mathbb {R}}^ 2$.
For a rectangular domain $[a, b]{\times}[c, d]{\subset}{\mathbb {R}}^ 2$, we consider the …

We define a family of curves, the n-catenaries, parameterized by the nonzero reals. They
include the classical catenaries (n= 1), parabolas (n= 1/2), cycloids (n=− 1/2), and …

In this paper, the notion of the catenary curve in the sphere and in the hyperbolic plane is
introduced. In both spaces, a catenary is defined as the shape of a hanging chain when its …

For every interval [a, b], we denote by (xA, yA) and (xL, yL) the geometric centroid of the area
under a catenary y= k cosh ((xc)/k) defined on this interval and the centroid of the curve itself …

Volume/Surface Area Relations for <italic>n</italic>-Dimensional Spheres, Pseudospheres,
and Catenoids Page 1 Volume/Surface Area Relations for n-Dimensional Spheres …