Discrete Spin Geometry for Surfaces

Ye, Zi

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Original title:: Discrete Spin Geometry for Surfaces
Translated title:: Diskrete Spin-Geometrie für Flächen
Author:: Ye, Zi
Year:: 2020
Document type:: Dissertation
Faculty/School:: Fakultät für Mathematik
Advisor:: Hoffmann, Tim N. (Prof. Dr.)
Referee:: Hoffmann, Tim N. (Prof. Dr.); Pinkall, Ulrich (Prof.Dr.); Wardetzky, Max (Prof.Dr.)
Language:: en
Subject group:: MAT Mathematik
Keywords:: Discrete Differential Geometry, Spin Geometry, Geometry Processing
Translated keywords:: Diskrete Differentialgeometrie, Spin-Geometrie, Geometrieverarbeitung
TUM classification:: MAT 500d
Abstract:: This thesis proposes a discrete framework for spin geometry of surfaces. Specifically, we discretize the basic notions in spin geometry, such as the spin structure, spin connection and Dirac operator. In this framework, two types of Dirac operators are closely related as in smooth case. Moreover, they both induce the discrete conformal immersion with prescribed mean curvature half-density.
Translated abstract:: In dieser Arbeit wird ein diskreter Zugang zur Spin-Geometrie vorgestellt. Insbesondere diskretisieren wir die grundlegende Begriffe, wie zum Beispiel die Spin-Struktur, den Spin-Zusammenhang und den Dirac Operator. In diesem Rahmen sind zwei Varianten für den Dirac Operator eng verwandt wie in der glatten Theorie. Darüber hinaus induzieren beide die diskret-konforme Immersion mit vorgeschriebener Halbdichte der mittleren Krümmung.
WWW:: https://mediatum.ub.tum.de/?id=1531414
Date of submission:: 17.12.2019
Oral examination:: 08.05.2020
File size:: 62009046 bytes
Pages:: 124
Urn (citeable URL):: https://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:91-diss-20200508-1531414-1-3
Last change:: 24.06.2020
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