On discrete differential geometry in twistor space

JOURNAL OF GEOMETRY AND PHYSICS

卷:68

Article

关键词: Discrete differential geometry;    Discrete integrable systems;    Plucker quadric;    Conformal differential geometry;    Quaternionic projective space;    Cross-ratio;   

DOI  :  10.1016/j.geomphys.2013.02.008

来源: Elsevier

【 摘 要 】

In this paper we introduce a discrete integrable system generalizing the discrete (real) cross-ratio system in S-4 to complex values of a generalized cross-ratio by considering S-4 as a real section of the complex Plucker quadric, realized as the space of two-spheres in S-4. We develop the geometry of the Plucker quadric by examining the novel contact properties of two-spheres in S-4, generalizing classical Lie geometry in S-3. Discrete differential geometry aims to develop discrete equivalents of the geometric notions And methods of classical differential geometry. We define discrete principal contact element nets for the Plucker quadric and prove several elementary results. Employing a second real structure, we show that these results generalize previous results by Bobenko and Suns (2007) [18] on discrete differential geometry in the Lie quadric. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free