The dual curve and the Plücker formulas

2001 ◽  
pp. 73-94
Author(s):  
Gerd Fischer
Keyword(s):  
Dual Curve

Singularities and dualities of pedal curves in pseudo-hyperbolic and de Sitter space

2020 ◽  
Vol 18 (01) ◽  
pp. 2150008
Author(s):  
Yanlin Li ◽  
Yushu Zhu ◽  
Qing-You Sun
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Normal Forms ◽  
De Sitter Space ◽  
Closed String ◽  
Condensation Process ◽  
De Sitter ◽  
Unit Speed ◽  
Dual Curve ◽  
Pedal Curve

For the spherical unit speed nonlightlike curve in pseudo-hyperbolic space and de Sitter space [Formula: see text] and a given point P, we can define naturally the pedal curve of [Formula: see text] relative to the pedal point P. When the pseudo-sphere dual curve germs are nonsingular, singularity types of such pedal curves depend only on locations of pedal points. In this paper, we give a complete list of normal forms for singularities and locations of pedal points when the pseudo-sphere dual curve germs are nonsingular. Furthermore, we obtain the extension results in dualities, which has wide influence on the open and closed string field theory and string dynamics in physics, and can be used to better solve the dynamics of trajectory particle condensation process.

scholarly journals Singularities of pedal curves produced by singular dual curve germs in Sn

2010 ◽  
Vol 43 (2) ◽  
Author(s):  
Takashi Nishimura
Keyword(s):  
Dual Curve

AbstractFor an

Vectorial moments of curves in Euclidean 3-space

2017 ◽  
Vol 14 (02) ◽  
pp. 1750020 ◽  
Author(s):  
Yılmaz Tunçer
Keyword(s):  
Regular Curve ◽  
Constant Breadth ◽  
Dual Curve

In this study, we introduced the vectorial moments as a new curves as [Formula: see text]-dual curve, where [Formula: see text], constructed by the Frenet vectors of a regular curve in Euclidean 3-space and we gave the Frenet apparatus of [Formula: see text]-dual curves and also we applied to helices and curve pairs of constant breadth.

A Note on Dual-Curve Construction: Mr. Crab’s Bootstrap

2014 ◽  
Vol 22 (2) ◽  
pp. 105-132 ◽  
Author(s):  
Roberto Baviera ◽  
Alessandro Cassaro
Keyword(s):  
Dual Curve
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