Minimal Lagrangian surfaces in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si2.svg"><mml:mrow><mml:mi>ℂ</mml:mi><mml:msup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> via the loop group method Part I: The contractible case

Dorfmeister, Josef; Ma, Hui

doi:10.1016/j.geomphys.2020.104016

Journal of Geometry and Physics

2021

DOI: 10.1016/j.geomphys.2020.104016

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Minimal Lagrangian surfaces in ℂP2 via the loop group method Part I: The contractible case

Josef Dorfmeister

Hui Ma

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Cited by 2 publications

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Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space

Dorfmesiter

Kobayashi

2020

Annali di Matematica

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It has been known for some time that there exist 5 essentially different real forms of the complex affine Kac-Moody algebra of type A(2) 2 and that one can associate 4 of these real forms with certain classes of "integrable surfaces", such as minimal Lagrangian surfaces in CP 2 and CH 2 , as well as definite and indefinite affine spheres in R 3 .In this paper we consider the class of timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space CH 2 1 . We show that this class of surfaces corresponds to the fifth real form.Moreover, for each timelike Lagrangian surface in CH 2 1 we define natural Gauss maps into certain homogeneous spaces and prove a Ruh-Vilms type theorem, characterizing timelike minimal Lagrangian surfaces among all timelike Lagrangian surfaces in terms of the harmonicity of these Gauss maps.

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Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space

Dorfmesiter

Kobayashi

2020

Annali di Matematica

Self Cite

View full text Add to dashboard Cite

show abstract

Minimal Lagrangian surfaces in CP2 via the loop group method part II: The general case

Dorfmeister,

2025

Journal of Geometry and Physics

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Minimal Lagrangian surfaces in ℂP2 via the loop group method Part I: The contractible case

Cited by 2 publications

References 20 publications

Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space

Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space

Minimal Lagrangian surfaces in CP2 via the loop group method part II: The general case

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