Isometric embedding inR 3 of complete noncompact nonnegatively curved surfaces

1997 ◽  
Vol 94 (1) ◽  
pp. 271-286 ◽  
Author(s):  
Hong Jiaxing
Keyword(s):  
Isometric Embedding ◽  
Curved Surfaces

Flexible Sensors for NDI of Curved Surfaces on Turbofan Components

2018 ◽  
Author(s):  
Evan Weststrate ◽  
◽  
Michael S. Squillante ◽  
Sergey Chekanov
Keyword(s):  
Curved Surfaces ◽  
Flexible Sensors

scholarly journals An Intrinsic Characterization of Five Points in a CAT(0) Space

2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda
Keyword(s):  
Metric Space ◽  
Isometric Embedding ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
New Approach ◽  
Intrinsic Characterization ◽  
New Family

AbstractGromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.

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