lagrangian singularities
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Lagrangian singularities

2012 ◽  
pp. 287-297
Author(s):  
V. I. Arnold ◽  
S. M. Gusein-Zade ◽  
A. N. Varchenko
Keyword(s):  
Lagrangian Singularities

scholarly journals SINGULARITIES OF EVOLUTES OF HYPERSURFACES IN HYPERBOLIC SPACE

2004 ◽  
Vol 47 (1) ◽  
pp. 131-153 ◽  
Author(s):  
Shyuichi Izumiya ◽  
Donghe Pei ◽  
Masatomo Takahashi
Keyword(s):  
Differential Geometry ◽  
Hyperbolic Space ◽  
Subject Classification ◽  
Primary 53A35 ◽  
Lagrangian Singularities

AbstractWe study the differential geometry of hypersurfaces in hyperbolic space. As an application of the theory of Lagrangian singularities, we investigate the contact of hypersurfaces with families of hyperspheres or equidistant hyperplanes.AMS 2000 Mathematics subject classification: Primary 53A35. Secondary 58C27

Singularities of line congruences

2003 ◽  
Vol 133 (6) ◽  
pp. 1341-1359 ◽  
Author(s):  
Shyuichi Izumiya ◽  
Kentaro Saji ◽  
Nobuko Takeuchi
Keyword(s):  
Three Dimensional ◽  
Parameter Family ◽  
General Line ◽  
Line Congruence ◽  
Lagrangian Singularities ◽  
Generic Singularities ◽  
Two Parameter

A line congruence is a two-parameter family of lines in R3. In this paper we study singularities of line congruences. We show that generic singularities of general line congruences are the same as those of stable mappings between three-dimensional manifolds. Moreover, we also study singularities of normal congruences and equiaffine normal congruences from the viewpoint of the theory of Lagrangian singularities.

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