Paper's Title:

On the Equiform Geometry of the Involute-evolute Curve Couple in Hyperbolic and de Sitter Spaces

Author(s):

M. Khalifa Saad, H. S. Abdel-Aziz and A. A. Abdel-Salam

Department of Mathematics,
Faculty of Science,
Islamic University of Madinah,
KSA.
E-mail: mohammed.khalifa@iu.edu.sa

Department of Mathematics,
Faculty of Science,
Sohag University, Sohag,
EGYPT.
E-mail: habdelaziz2005@yahoo.com

Department of Mathematics,
Faculty of Science,
Sohag University, Sohag,
EGYPT.
E-mail: asem2e@yahoo.com

Abstract:

In this paper, we aim to investigate the equiform differential geometric properties of the involute-evolute curve couple with constant equiform curvatures in three-dimensional 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 Quasi-Frame in Euclidean 3-Space

Author(s):

M. Khalifa Saad and R. A. Abdel-Baky

Department of Mathematics, Faculty of Science,
Islamic University of Madinah,
KSA.
Department of Mathematics, Faculty of Science,
Sohag University, Sohag,
EGYPT.
E-mail: mohamed_khalifa77@science.sohag.edu.eg, mohammed.khalifa@iu.edu.sa

Department of Mathematics, Faculty of Science,
Assiut University, Assiut,
EGYPT.
E-mail: rbaky@live.com

Abstract:

This paper aims to study the skew ruled surfaces by using the quasi-frame of Smarandache curves in the Euclidean 3-space. Also, we reveal the relationship between Serret-Frenet and quasi-frames and give a parametric representation of a directional ruled surface using the quasi-frame. Besides, some comparative examples are given and plotted which support our method and main results.

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