Singularities and Bifurcations of Pseudospherical Surfaces

David Brander; Farid Tari

doi:10.14760/OWP-2020-08

Singularities and Bifurcations of Pseudospherical Surfaces

David Brander, Farid Tari

Universidade de São Paulo

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Abstract

We study singularities and bifurcations of constant negative curvature surfaces in Euclidean 3-space via their association with Lorentzian harmonic maps. This preprint presents the basic results on this, the full proofs of which will appear in an article under preparation. We show that the generic bifurcations in 1-parameter families of such surfaces are the Cuspidal Butterfly, Cuspidal Lips, Cuspidal Beaks, 2/5 Cuspidal edge and Shcherbak bifurcations

Original language	English
Journal	Oberwolfach Preprints
Volume	2020
Issue number	08
Number of pages	7
ISSN	1864-7596
DOIs	https://doi.org/10.14760/OWP-2020-08
Publication status	Published - 2020

Keywords

Bifurcations
Constant Gauss curvature
Cauchy problem
Differential geometry
Discriminants
Frontals
Integrable systems
Loop groups
Pseudospherical surfaces
Singularities
Wave fronts
Wave maps

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10.14760/OWP-2020-08

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Geometry and Lorentzian harmonic maps
Brander, D. (PI)
01/07/2019 → 30/06/2023
Project: Research

Cite this

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abstract = "We study singularities and bifurcations of constant negative curvature surfaces in Euclidean 3-space via their association with Lorentzian harmonic maps. This preprint presents the basic results on this, the full proofs of which will appear in an article under preparation. We show that the generic bifurcations in 1-parameter families of such surfaces are the Cuspidal Butterfly, Cuspidal Lips, Cuspidal Beaks, 2/5 Cuspidal edge and Shcherbak bifurcations",

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AB - We study singularities and bifurcations of constant negative curvature surfaces in Euclidean 3-space via their association with Lorentzian harmonic maps. This preprint presents the basic results on this, the full proofs of which will appear in an article under preparation. We show that the generic bifurcations in 1-parameter families of such surfaces are the Cuspidal Butterfly, Cuspidal Lips, Cuspidal Beaks, 2/5 Cuspidal edge and Shcherbak bifurcations

KW - Bifurcations

KW - Constant Gauss curvature

KW - Cauchy problem

KW - Differential geometry

KW - Discriminants

KW - Frontals

KW - Integrable systems

KW - Loop groups

KW - Pseudospherical surfaces

KW - Singularities

KW - Wave fronts

KW - Wave maps

U2 - 10.14760/OWP-2020-08

DO - 10.14760/OWP-2020-08

M3 - Journal article

SN - 1864-7596

VL - 2020

JO - Oberwolfach Preprints

JF - Oberwolfach Preprints

IS - 08

ER -

Singularities and Bifurcations of Pseudospherical Surfaces

Abstract

Keywords

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Projects

Geometry and Lorentzian harmonic maps

Cite this