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On Discrete Differential Geometry in Twistor Space
- Publication Year :
- 2011
-
Abstract
- 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 Pl\"ucker quadric, realized as the space of two-spheres in $S^4.$ We develop the geometry of the Pl\"ucker 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 Pl\"ucker quadric and prove several elementary results. Employing a second real real structure, we show that these results generalize previous results by Bobenko and Suris $(2007)$ on discrete differential geometry in the Lie quadric.<br />Comment: 32 pages, 11 figures
- Subjects :
- Mathematics - Differential Geometry
Pure mathematics
Quadric
Integrable system
53A30
Cross-ratio
General Physics and Astronomy
Mathematics::Algebraic Geometry
Differential geometry
Differential Geometry (math.DG)
FOS: Mathematics
Twistor space
Geometry and Topology
Discrete differential geometry
Plucker
Quaternionic projective space
Mathematical Physics
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....6136cf3c45aaca0ccd004e250135fe95