• Corpus ID: 233481530

Channel linear Weingarten surfaces in space forms

  title={Channel linear Weingarten surfaces in space forms},
  author={Udo Hertrich-Jeromin and Mason Pember and Denis Polly},
Channel linear Weingarten surfaces in space forms are investigated in a Lie sphere geometric setting, which allows for a uniform treatment of different ambient geometries. We show that any channel linear Weingarten surface in a space form is isothermic and, in particular, a surface of revolution in its ambient space form. We obtain explicit parametrisations for channel surfaces of constant Gauss curvature in space forms, and thereby for a large class of linear Weingarten surfaces up to parallel… 
2 Citations

Figures and Tables from this paper

Symmetry breaking in geometry

. A geometric mechanism that may, in analogy to similar notions in physics, be considered as “symmetry breaking” in geometry is described, and several instances of this mechanism in differential

Constrained elastic curves and surfaces with spherical curvature lines

In this paper we consider surfaces with one or two families of spherical curvature lines. We show that every surface with a family of spherical curvature lines can locally be generated by a pair of



Channel linear Weingarten surfaces

We demonstrate that every non-tubular channel linear Weingarten surface in Euclidean space is a surface of revolution, hence parallel to a catenoid or a rotational surface of non-zero constant Gauss

Lie geometry of linear Weingarten surfaces

Rotational Weingarten surfaces in hyperbolic 3-space

We study rotational Weingarten surfaces in the hyperbolic space $$\mathbb {H}^3(-1)$$ H 3 ( - 1 ) with the principal curvatures $$\kappa $$ κ and $$\lambda $$ λ satisfying a certain functional

Delaunay surfaces in S3(ρ)

Recently, invariant constant mean curvature (CMC) surfaces in real space forms have been characterized locally by using extremal curves of a Blaschke type energy functional [5]. Here, we use this

A variational characterization of profile curves of invariant linear Weingarten surfaces

  • Á. Pámpano
  • Mathematics
    Differential Geometry and its Applications
  • 2020

Sur la surface de révolution dont la courbure moyenne est constante.

Spherical surfaces with constant mean curvature in hyperbolic space

Parabolic surfaces in hyperbolic space with constant Gaussian curvature

A parabolic surface in hyperbolic space H 3 is a surface invariant by a group of parabolic isometries. In this paper we describe all parabolic surfaces with constant Gaussian curvature. We study the