Infinitesimal conformal deformations of triangulated surfaces in space
Abstract
We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is conformal if it preserves length cross-ratios. On one hand, conformal deformations generalize deformations preserving edge lengths. On the other hand, there is a one-to-one correspondence between infinitesimal conformal deformations in space and infinitesimal isometric deformations of the stereographic image on the sphere. The space of infinitesimal conformal deformations can be parametrized in terms of the change in dihedral angles, which is closely related to the Schl\"{a}fli formula.
Keywords
Cite
@article{arxiv.1702.04019,
title = {Infinitesimal conformal deformations of triangulated surfaces in space},
author = {Wai Yeung Lam and Ulrich Pinkall},
journal= {arXiv preprint arXiv:1702.04019},
year = {2018}
}
Comments
21 pages. v3. revised. Corollary 8.8 is added. To appear in Discrete & Computational Geometry