STABILITY OF SURFACES WITH CONSTANT MEAN CURVATURE IN THREE-DIMENSIONAL SPACE FORMS

2002 ◽  
Author(s):  
MIYUKI KOISO
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Forms ◽  
Three Dimensional Space

scholarly journals Harmonic morphisms and conformal foliations by geodesics of three-dimensional space forms

1991 ◽  
Vol 51 (1) ◽  
pp. 118-153 ◽  
Author(s):  
Paul Baird ◽  
John C. Wood
Keyword(s):  
Space Form ◽  
Holomorphic Mapping ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Classification ◽  
Harmonic Morphisms ◽  
Connected Space ◽  
Space Forms ◽  
Simply Connected ◽  
Three Dimensional Space

AbstractA complete classification is given of harmonic morphisms to a surface and conformal foliations by geodesics, with or without isolated singularities, of a simply-connected space form. The method is to associate to any such a holomorphic map from a Riemann surface into the space of geodesics of the space form. Properties such as nonintersecting fibres (or leaves) are translated into conditions on the holomorphic mapping which show it must have a simple form corresponding to a standard example.

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