Abstract
This paper studies the geometry of pseudospherical surfaces from the point of view of Lorentz harmonic maps from the Minkowski plane into S2. 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.
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Communicated by D. Ferus
Supported by DFG grants Pi 158/2 – 1 & 158/2–2.
Partially supported by DFG grants Pi 158/2–1 & 158/2–2.
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Melko, M., Sterling, I. Application of soliton theory to the construction of pseudospherical surfaces in R3 . Ann Glob Anal Geom 11, 65–107 (1993). https://doi.org/10.1007/BF00773365
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DOI: https://doi.org/10.1007/BF00773365