Lie transformation groups and differential geometry

1987 ◽  
pp. 34-52 ◽  
Author(s):  
Wu-Yi Hsiang
Keyword(s):  
Differential Geometry ◽  
Transformation Groups ◽  
Lie Transformation

A theory of extended lie transformation groups

1963 ◽  
Vol 61 (1) ◽  
pp. 247-333
Author(s):  
Tsurusaburo Takasu
Keyword(s):  
Transformation Groups ◽  
Lie Transformation

Visual Illusions of Angle as an Application of Lie Transformation Groups

SIAM Review ◽  
1971 ◽  
Vol 13 (2) ◽  
pp. 169-184 ◽  
Author(s):  
William C. Hoffman
Keyword(s):  
Visual Illusions ◽  
Transformation Groups ◽  
Lie Transformation

Lie Transformation Groups and Geometry

2012 ◽  
Author(s):  
Andreas Arvanitoyeorgos
Keyword(s):  
Transformation Groups ◽  
Lie Transformation

Pattern Recognition in Kittens: Performance on Lie Patterns

Perception ◽  
1983 ◽  
Vol 12 (4) ◽  
pp. 393-410 ◽  
Author(s):  
Peter C Dodwell ◽  
Frances E Wilkinson ◽  
Michael W von Grünau
Keyword(s):  
Experimental Study ◽  
Pattern Recognition ◽  
Pattern Analysis ◽  
Transformation Group ◽  
Transformation Groups ◽  
Continuous Transformation ◽  
Anatomy And Physiology ◽  
Visual Behaviour ◽  
Lie Transformation ◽  
Pattern Information

Despite a vast accumulation of knowledge about the anatomy and physiology of the cat's visual system in recent years, and about its early development, there has been very little experimental study of the development of visual behaviour in this species. This is especially true of the kitten's ability to recognize patterns. Two experiments are reported that aim to remedy some part of this deficiency, and that also serves to examine a particular hypothesis about the basis of pattern analysis in the young organism. This is Hoffman's hypothesis that the orbits of elementary Lie transformation groups (a species of continuous transformation group) represent the basis for coding pattern information.

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