scholarly journals A loop group method for minimal surfaces in the three-dimensional Heisenberg group

2016 ◽  
Vol 20 (3) ◽  
pp. 409-448
Author(s):  
Josef F. Dorfmeister ◽  
Jun-Ichi Inoguchi ◽  
Shimpei Kobayashi
Keyword(s):  
Heisenberg Group ◽  
Minimal Surfaces ◽  
Three Dimensional ◽  
Loop Group ◽  
Group Method

scholarly journals Ruled minimal surfaces in the three-dimensional Heisenberg group

2013 ◽  
Vol 261 (2) ◽  
pp. 477-496 ◽  
Author(s):  
Heayong Shin ◽  
Young Wook Kim ◽  
Sung-Eun Koh ◽  
Hyung Yong Lee ◽  
Seong-Deog Yang
Keyword(s):  
Heisenberg Group ◽  
Minimal Surfaces ◽  
Three Dimensional

scholarly journals On the Bernstein Problem in the Three-dimensional Heisenberg Group

2016 ◽  
Vol 59 (01) ◽  
pp. 50-61
Author(s):  
Josef F. Dorfmeister ◽  
Jun-ichi Inoguchi ◽  
Shimpei Kobayashi
Keyword(s):  
Heisenberg Group ◽  
Three Dimensional ◽  
Loop Group ◽  
Alternative Proof ◽  
Geometric Meaning ◽  
Bernstein Problem ◽  
Minimal Graphs ◽  
Simple Alternative ◽  
Two Parameter ◽  
Group Technique

Abstract In this note we present a simple alternative proof for the Bernstein problem in the threedimensional Heisenberg group Nil3 by using the loop group technique. We clarify the geometric meaning of the two-parameter ambiguity of entire minimal graphs with prescribed Abresch- Rosenberg diòerential.

scholarly journals The Björling problem for minimal surfaces in a Lorentzian three-dimensional Lie group

2014 ◽  
Vol 195 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Adriana A. Cintra ◽  
Francesco Mercuri ◽  
Irene I. Onnis
Keyword(s):  
Lie Group ◽  
Minimal Surfaces ◽  
Three Dimensional ◽  
Björling Problem

scholarly journals Einstein–Weyl geometry, dispersionless Hirota equation and Veronese webs

2014 ◽  
Vol 157 (1) ◽  
pp. 139-150 ◽  
Author(s):  
MACIEJ DUNAJSKI ◽  
WOJCIECH KRYŃSKI
Keyword(s):  
Heisenberg Group ◽  
Twistor Space ◽  
Three Dimensional ◽  
Poisson Structures ◽  
Weyl Geometry ◽  
Hirota Equation ◽  
Five Dimensions ◽  
Dispersionless Hirota Equation

AbstractWe exploit the correspondence between the three–dimensional Lorentzian Einstein–Weyl geometries of the hyper–CR type and the Veronese webs to show that the former structures are locally given in terms of solutions to the dispersionless Hirota equation. We also demonstrate how to construct hyper–CR Einstein–Weyl structures by Kodaira deformations of the flat twistor space$T\mathbb{CP}^1$, and how to recover the pencil of Poisson structures in five dimensions illustrating the method by an example of the Veronese web on the Heisenberg group.

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