Discrete Weierstrass-type representations

Abstract

Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We show that the known discrete Weierstrass-type representations of certain surface classes can be viewed as applications of the $\Omega$-dual transform to lightlike Gauss maps in Laguerre geometry. From this construction, further Weierstrass-type representations arise. As an application of the techniques we develop, we show that all discrete linear Weingarten surfaces of Bryant or Bianchi type locally arise via Weierstrass-type representations from discrete holomorhpic maps.

22 pages, 4 figures

References in corpus (2)

• Discrete cyclic systems and circle congruences
• Notes on flat fronts in hyperbolic space

Cited by in corpus (3)

• Periodic discrete Darboux transforms
• Notes on flat fronts in hyperbolic space
• Spinor representation in isotropic 3-space via Laguerre geometry