conformal gauss map
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Author(s):  
Jianbo Fang ◽  
Lin Liang


2020 ◽  
pp. 1-25
Author(s):  
JOSEF F. DORFMEISTER ◽  
PENG WANG

A Willmore surface $y:M\rightarrow S^{n+2}$ has a natural harmonic oriented conformal Gauss map $Gr_{y}:M\rightarrow SO^{+}(1,n+3)/SO(1,3)\times SO(n)$ , which maps each point $p\in M$ to its oriented mean curvature 2-sphere at $p$ . An easy observation shows that all conformal Gauss maps of Willmore surfaces satisfy a restricted nilpotency condition, which will be called “strongly conformally harmonic.” The goal of this paper is to characterize those strongly conformally harmonic maps from a Riemann surface $M$ to $SO^{+}(1,n+3)/SO^{+}(1,3)\times SO(n)$ , which are the conformal Gauss maps of some Willmore surface in $S^{n+2}.$ It turns out that generically, the condition of being strongly conformally harmonic suffices to be associated with a Willmore surface. The exceptional case will also be discussed.







1987 ◽  
Vol 5 (2) ◽  
pp. 97-116 ◽  
Author(s):  
Marco Rigoli


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