Multi-local singularities of k-folding maps on curves and surfaces.
Geometry of manifolds in the euclidian space and in the Minkowski space
Variational and topological methods for partial differential equation
| Full text | |
| Author(s): |
Brander, David
;
Tari, Farid
Total Authors: 2
|
| Document type: | Journal article |
| Source: | ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE; v. 23, n. 1, p. 37-pg., 2022-01-01. |
| Abstract | |
Wave maps (or Lorentzian-harmonic maps) from a 1 + 1-dimensional Lorentz space into the 2-sphere are associated to constant negative Gaussian curvature surfaces in Euclidean 3-space via the Gauss map, which is harmonic with respect to the metric induced by the second fundamental form. We give a method for constructing germs of analytic Lorentzian-harmonic maps from their k-jets and use this construction to study the singularities of such maps. We also show how to construct pseudospherical surfaces with prescribed singularities using loop groups. We study the singularities of pseudospherical surfaces and obtain their bifurcations in generic 1-parameter families of such surfaces. (AU) | |
| FAPESP's process: | 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision |
| Grantee: | Farid Tari |
| Support Opportunities: | Research Projects - Thematic Grants |