scholarly journals Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor

2012 ◽  
Vol 193 (2) ◽  
pp. 529-550 ◽  
Author(s):  
R. Caddeo ◽  
S. Montaldo ◽  
C. Oniciuc ◽  
P. Piu
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Space Forms ◽  
Divergence Free ◽  
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.

scholarly journals Function-theoretic Properties for the Gauss Maps of Various Classes of Surfaces

2015 ◽  
Vol 67 (6) ◽  
pp. 1411-1434 ◽  
Author(s):  
Yu Kawakami
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Space Forms ◽  
Flat Surfaces ◽  
Immersed Surfaces ◽  
Gauss Maps ◽  
Improper Affine Spheres ◽  
Euclidean Three Space ◽  
Three Space ◽  
Three Dimensional Space

AbstractWe elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine spheres in the affine three-space, and constant mean curvature one surfaces and flat surfaces in hyperbolic three-space. To achieve this purpose, we prove an optimal curvature bound for a specified conformal metric on an open Riemann surface and give some applications. We also provide unicity theorems for the Gauss maps of these classes of surfaces.

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