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

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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Veröffentlicht in:Computers, materials & continua materials & continua, 2018-01, Vol.57 (3), p.389-415
Hauptverfasser: S. Abdel-Aziz, H., Khalifa Saad and A. A. Abdel-Salam, M.
Format: Artikel
Sprache:eng
Schlagworte:
Curves
Invariants
Singularities
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Zusammenfassung: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