三维海森堡群中具有非平凡几何的极小曲面

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2022-01-01 DOI:10.1515/coma-2021-0141

J. Dorfmeister, J. Inoguchi, Shimpei Kobayashi

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引用次数: 2

摘要

摘要我们使用广义Weierstrass型表示，即所谓的环群方法，研究了三维Heisenberg群Nil3中的对称极小曲面。特别地，我们将提出一个如何在Nil3中构造具有非平凡几何的极小曲面的一般方案。将特别强调等变极小曲面。此外，我们将对等距群Iso的单参数子群给出的等变极小曲面进行分类◦（无3），共无3。

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Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group

Abstract We study symmetric minimal surfaces in the three-dimensional Heisenberg group Nil3 using the generalized Weierstrass type representation, the so-called loop group method. In particular, we will present a general scheme for how to construct minimal surfaces in Nil3 with non-trivial geometry. Special emphasis will be put on equivariant minimal surfaces. Moreover, we will classify equivariant minimal surfaces given by one-parameter subgroups of the isometry group Iso◦(Nil3) of Nil3.

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.