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Transformations on Willmore surfaces Katrin Leschke
 

Summary: Transformations on Willmore surfaces
Katrin Leschke
Habilitationsschrift zur Erlangung der Venia Legendi, eingereicht an der
mathematisch­naturwissenschaftlichen Fakult¨at der Universit¨at Augsburg
17. Mai 2006
2
Contents
0 Introduction 5
1 Quaternionic Holomorphic Geometry 13
1.1 Holomorphic curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.1.1 Conformal maps into the 4­sphere . . . . . . . . . . . . . . . . . . 14
1.1.2 Holomorphic curves in HPn . . . . . . . . . . . . . . . . . . . . . . 24
1.1.3 Frenet curves in HPn . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.2 Holomorphic line bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.2.1 Holomorphic vector bundles . . . . . . . . . . . . . . . . . . . . . . 35
1.2.2 The Kodaira correspondence . . . . . . . . . . . . . . . . . . . . . 38
1.2.3 The Riemann­Roch Theorem . . . . . . . . . . . . . . . . . . . . . 41
1.2.4 The Pl¨ucker formula . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2 Transformations on conformal maps 47
2.1 The Darboux transformation . . . . . . . . . . . . . . . . . . . . . . . . . 47

  

Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield

 

Collections: Mathematics