A rank 2 theory for constrained Willmore tori in the 3-dimensional sphere

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dc.identifier.uri http://dx.doi.org/10.15488/11029
dc.identifier.uri https://www.repo.uni-hannover.de/handle/123456789/11111
dc.contributor.advisor Heller, Lynn
dc.contributor.author Heydel, Max Christian eng
dc.date.accessioned 2021-06-04T08:16:08Z
dc.date.available 2021-06-04T08:16:08Z
dc.date.issued 2021
dc.identifier.citation Heydel, Max Christian: A rank 2 theory for constrained Willmore tori in the 3-dimensional sphere. Hannover : Gottfried Wilhelm Leibniz Universität, Diss., 2021, iii, 107 S. DOI: https://doi.org/10.15488/11029 eng
dc.description.abstract The main subject of this thesis are constrained Willmore tori in the 3-dimensional sphere S^3. It is known that constrained Willmore tori in the 4-sphere come with an associated C_∗-family of flat SL(4,C)-connections. This allows to study constrained Willmore tori as an integrable system. The initial surface can be reconstructed by holomorphic data on the spectralcurve Σ, which is the riemann surface on which the eigenlines of the family of connections are well-defined. If the constrained Willmore torus lies in a 3-dimensional sphere, there is a further symmetry on the spectral curve, a holomorphic involution σ. In this thesis we show that this involution allows to reduce the family of SL(4,C)-connections into a family of SL(2,C)-connections. We achieve this by pushing forward the eigenline bundle of the rank 4 family on the quotient surface Σ/σ. Therefore,the rank 2 family of connections is a Σ/σ-family of connections, which is a hyperelliptic surface. The rank 2 family of connections then allows to give a Sym-Bobenko formula, similiar to the case of constant mean curvature surfaces in S^3. Further, if the quotient surface Σ/σ=CP1, the surface is of constant mean curvature in a space form. eng
dc.language.iso eng eng
dc.publisher Hannover : Institutionelles Repositorium der Leibniz Universität Hannover
dc.rights CC BY 3.0 DE eng
dc.rights.uri http://creativecommons.org/licenses/by/3.0/de/ eng
dc.subject Constrained Willmore torus eng
dc.subject Integrable system eng
dc.subject Sym-Bobenko formula eng
dc.subject Quaternionic surface theory eng
dc.subject Constrained Willmore Torus, ger
dc.subject Sym-Bobenko Formel ger
dc.subject Integrables System ger
dc.subject Quaternionische Flächentheorie ger
dc.subject.ddc 510 | Mathematik eng
dc.title A rank 2 theory for constrained Willmore tori in the 3-dimensional sphere eng
dc.type doctoralThesis eng
dc.type Text eng
dc.description.version publishedVersion eng
tib.accessRights frei zug�nglich eng

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