A new variational characterization of three-dimensional space forms

2001 ◽  
Vol 145 (2) ◽  
pp. 251-278 ◽  
Author(s):  
Matthew J. Gursky ◽  
Jeff A. Viaclovsky
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Variational Characterization ◽  
Space Forms ◽  
Three Dimensional Space

scholarly journals Isothermic surfaces in sphere geometries as Moutard nets

2007 ◽  
Vol 463 (2088) ◽  
pp. 3171-3193 ◽  
Author(s):  
Alexander I Bobenko ◽  
Yuri B Suris
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauss Map ◽  
Point Property ◽  
Property A ◽  
Lie Geometry ◽  
Möbius Geometry ◽  
Isothermic Surfaces ◽  
Three Dimensional Space

We give an elaborated treatment of discrete isothermic surfaces and their analogues in different geometries (projective, Möbius, Laguerre and Lie). We find the core of the theory to be a novel characterization of discrete isothermic nets as Moutard nets. The latter are characterized by the existence of representatives in the space of homogeneous coordinates satisfying the discrete Moutard equation. Moutard nets admit also a projective geometric characterization as nets with planar faces with a five-point property: a vertex and its four diagonal neighbours span a three-dimensional space. Restricting the projective theory to quadrics, we obtain Moutard nets in sphere geometries. In particular, Moutard nets in Möbius geometry are shown to coincide with discrete isothermic nets. The five-point property, in this particular case, states that a vertex and its four diagonal neighbours lie on a common sphere, which is a novel characterization of discrete isothermic surfaces. Discrete Laguerre isothermic surfaces are defined through the corresponding five-plane property, which requires that a plane and its four diagonal neighbours share a common touching sphere. Equivalently, Laguerre isothermic surfaces are characterized by having an isothermic Gauss map. S-isothermic surfaces as an instance of Moutard nets in Lie geometry are also discussed.

Spatial Kinematic Analysis of the Upper Extremity Using a Biplanar Videotaping Method

1981 ◽  
Vol 103 (1) ◽  
pp. 11-17 ◽  
Author(s):  
N. A. Langrana
Keyword(s):  
Upper Extremity ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Assistive Device ◽  
Kinematic Data ◽  
Computer Aided ◽  
Extremity Motion ◽  
Accuracy And Repeatability ◽  
Three Dimensional Space

A biplanar videotaping system is used to generate spatial kinematic data of an upper extremity motion. The technique is based upon the characterization of each segment by four points in three-dimensional space using biplanar videotaping and subsequent analysis by computer-aided descriptive geometry. The tests were conducted to determine the system’s accuracy and repeatability. The results of the joint kinematics of the test subjects performing a diagonal reaching activity with and without an orthosis (or an assistive device) are presented.

Energy Harvesting Aspects of Irregular Vibrating Forces Acting on Piezoelectric Devices

2015 ◽  
pp. 143-158
Author(s):  
Alessandro Massaro
Keyword(s):  
Energy Harvesting ◽  
Piezoelectric Materials ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Output Current ◽  
Vibrating System ◽  
External Forces ◽  
Piezoelectric Devices ◽  
Three Dimensional Space

After a brief introduction of piezoelectric materials, this chapter focuses on the characterization of vibrating freestanding piezoelectric AlN devices forced by different external forces acting simultaneously. The analyzed vibrating forces are applied mainly to piezoelectric freestanding structures stimulated by irregular vibration phenomena. Particular kinds of theoretical noise signals are commented. The goal of the chapter is to analyze the effect of the noise in order to model the chaotic vibrating system and to predict the output current signals. Moreover, the author also shows a possible alternative way to detect different vibrating force directions in the three dimensional space by means of curved piezoelectric layouts.

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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