The dual curve and the Plücker formulas

Author(s):  
Gerd Fischer
Keyword(s):  
2020 ◽  
Vol 18 (01) ◽  
pp. 2150008
Author(s):  
Yanlin Li ◽  
Yushu Zhu ◽  
Qing-You Sun

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.


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

AbstractFor an


2017 ◽  
Vol 14 (02) ◽  
pp. 1750020 ◽  
Author(s):  
Yılmaz Tunçer

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.


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

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