an:00727080
Zbl 0810.53003
Melko, M.; Sterling, I.
Application of soliton theory to the construction of pseudospherical surfaces in \(\mathbb{R}^ 3\)
EN
Ann. Global Anal. Geom. 11, No. 1, 65-107 (1993).
0232-704X 1572-9060
1993
j
53A05 35L70 35Q40
pseudospherical surfaces; Lorentz harmonic maps; Gauss map; soliton theory
Summary: This paper studies the geometry of pseudospherical surfaces from the point of view of Lorentz harmonic maps from the Minkowski plane into \(S^ 2\). After giving appropriate definitions, it is shown that such a map is the Gauss map of a pseudospherical surface. A natural subclass of harmonic maps is isolated and studied using well developed techniques of soliton theory. Then follows a numerical investigation based on these techniques. Examples that fall outside of the aforementioned subclass are also considered.