On a theorem by do Carmo and Dajczer

Haak, Guido

doi:10.1090/s0002-9939-98-04673-5

Cited by 4 publications

(1 citation statement)

References 7 publications

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“…From the harmonic map point of view, we notice the fundamental fact that the Gauss map of helicoidal CMC surfaces in R 3 , especially CMC surfaces of revolution in R 3 , are symmetric harmonic maps into the unit 2-sphere S 2 . Haak [30] gave an alternative proof of the do Carmo-Dajczer theorem by using the generalized Weierstrass type representation. The general theory of symmetry of CMC surfaces in R 3 is well organized [15,16].…”

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

Dorfmeister¹,

Inoguchi²,

Kobayashi³

2019

Preprint

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We study symmetric minimal surfaces in the three-dimensional Heisenberg group Nil 3 using the generalized Weierstrass type representation, the so-called loop group method. In particular, we will discuss how to construct minimal surfaces in Nil 3 with non-trivial topology. Moreover, we will classify equivariant minimal surfaces given by oneparameter subgroups of the isometry group Iso • (Nil 3 ) of Nil 3 .

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confidence: 99%

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

Dorfmeister¹,

Inoguchi²,

Kobayashi³

2019

Preprint

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Isometric deformations of the K14-flow translators in R3

Lee

2013

Comptes Rendus. Mathématique

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

2022

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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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On a theorem by do Carmo and Dajczer

Abstract: Abstract. We give a new proof of a theorem by M.P. do Carmo and M. Dajczer on helicoidal surfaces of constant mean curvature.

Cited by 4 publications

References 7 publications

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

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

Isometric deformations of the K14-flow translators in R3

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

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