


Paper's Title:
On the Equiform Geometry of the Involuteevolute Curve Couple in Hyperbolic and de Sitter Spaces
Author(s):
M. Khalifa Saad, H. S. AbdelAziz and A. A. AbdelSalam
Department of Mathematics,
Faculty of Science,
Islamic University of Madinah,
KSA.
Email: mohammed.khalifa@iu.edu.sa
Department of Mathematics,
Faculty of Science,
Sohag University, Sohag,
EGYPT.
Email: habdelaziz2005@yahoo.com
Department of Mathematics,
Faculty of Science,
Sohag University, Sohag,
EGYPT.
Email: asem2e@yahoo.com
Abstract:
In this paper, we aim to investigate the equiform differential geometric properties of the involuteevolute curve couple with constant equiform curvatures in threedimensional hyperbolic and de Sitter spaces. Also, we obtain some relations between the curvature functions of these curves and investigate some special curves with respect to their equiform curvatures. Finally, we defray two computational examples to support our main findings.
Paper's Title:
On Ruled Surfaces According to QuasiFrame in Euclidean 3Space
Author(s):
M. Khalifa Saad and R. A. AbdelBaky
Department of Mathematics, Faculty of
Science,
Islamic University of Madinah,
KSA.
Department of Mathematics, Faculty of Science,
Sohag University, Sohag,
EGYPT.
Email:
mohamed_khalifa77@science.sohag.edu.eg,
mohammed.khalifa@iu.edu.sa
Department of Mathematics, Faculty of
Science,
Assiut University, Assiut,
EGYPT.
Email: rbaky@live.com
Abstract:
This paper aims to study the skew ruled surfaces by using the quasiframe of Smarandache curves in the Euclidean 3space. Also, we reveal the relationship between SerretFrenet and quasiframes and give a parametric representation of a directional ruled surface using the quasiframe. Besides, some comparative examples are given and plotted which support our method and main results.
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