Deformation of Surfaces in Three-Dimensional Space Induced by Means of Integrable Systems
Journal of Advances in Mathematics and Computer Science · pp. 213–225 · Published 8 Dec 2012
10.9734/BJMCS/2012/1998Abstract
The correspondence between dierent versions of the Gauss-Weingarten equation is investigated. The compatibility condition for one version of the Gauss-Weingarten equation gives the Gauss-Mainardi-Codazzi system. A deformation of the surface is postulated which takes the same form as the original system but contains an evolution parameter. The compatibility condition of this new augmented system gives the deformed Gauss-Mainardi-Codazzi system. A Lax representation in terms of a spectral parameter associated with the deformed system is established. Several important examples of integrable equations based on the deformed system are then obtained. It is shown that the Gauss-Mainardi-Codazzi system can be obtained as a type of reduction of the self-dual Yang-Mills equations.
Cited by 0
No indexed citations yet.
Related research
- Strengthening Environmental Hygiene for Healthcare-associated Infections Prevention in Maternity Ward: Outstanding Findings from a Multisite Survey in the Ndé Division, West Cameroon — shares topic coverage
- Effect of Sodium Carboxymethyl Cellulose Concentration on the Photophysical Properties of Zinc Sulfide Nanoparticles — shares topic coverage
- Bacterial Contaminants on Exposed Surfaces and Their Antibiotic Sensitivity Patterns at the Benjamin Mkapa Hospital, Dodoma-Tanzania — shares topic coverage
- Distribution of Various Geochemical Forms of Potassium under Horticulture Land Use System of District Ganderbal — shares topic coverage
- Surface Characteristics of Tooth and Effectiveness of Diamond Points: A Systematic Review — shares topic coverage
Article metrics
Real usage data collected on this platform.
0
Page views
0
PDF downloads
0
Outbound clicks
0
Citations
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
No views recorded yet.
Traffic sources
Referring site, by host.
No traffic recorded yet.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.