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BY 4.0 license Open Access Published by De Gruyter Open Access November 15, 2022

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

  • Josef F. Dorfmeister , Jun-ichi Inoguchi and Shimpei Kobayashi
From the journal Complex Manifolds

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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Received: 2022-06-25
Accepted: 2022-10-15
Published Online: 2022-11-15

© 2022 Josef F. Dorfmeister et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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