Some Geometric Invariants of Pseudo-Spherical Evolutes in the Hyperbolic 3-Space

In this paper, we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space. We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invarian...

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Bibliographic Details
Published in:Computers, materials & continua materials & continua, 2018-01, Vol.57 (3), p.389-415
Main Authors: S. Abdel-Aziz, H., Khalifa Saad and A. A. Abdel-Salam, M.
Format: Article
Language:English
Subjects:
Curves
Invariants
Singularities
Citations: Items that cite this one
Online Access:Get full text
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Summary:In this paper, we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space. We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group. Besides, we defray with illustration some computational examples in support our main results.
ISSN:1546-2226
1546-2218
1546-2226
DOI:10.32604/cmc.2018.02149