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.

Analysis on Structure and Morphological of Carton Packaging

2013 ◽  
Vol 442 ◽  
pp. 338-341
Author(s):  
A Qiang Sun
Keyword(s):  
Structural Design ◽  
Body Shape ◽  
Space Form ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Body ◽  
Packaging Materials ◽  
Paper Study ◽  
Structural Morphology ◽  
Three Dimensional Space

The package structure is a three-dimensional space form, so people know the products are in used in the packaging. In packaging materials for paper use is very extensive, paper products are easy to shape the body shape for easy printing and recyclable advantage. This paper study design of the paper packaging structural, combining paper packaging structural design applications to explore the paper packaging structural morphology and environmentalist design consciousness.

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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