The Special Issues of Tbilisi Mathematical Journal are fully refereed international publications, publishing original research papers in all areas of pure and applied mathematics. The editors are well known experts in the field, particularly from leading universities of USA and Europe. Papers should satisfy high standards and only works of high quality are recommended for publication. They constitute a collection around selected themes related to mathematical sciences, or coming from a specific group of mathematicians or event, or coming from a workshop, symposia and international mathematical conferences.

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TBILISI - MATHEMATICS

Tbilisi Mathematical Journal

Special Issues, 1

Editor Hvedri Inassaridze

DOI 10.2478/9788395793882-fm

Special issue on 8th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2019), 27 – 30 August 2019, Baku, Azerbaijan

Lead Guest Editor: Murat Tosun (Sakarya University, Turkey) Guest Editors: Cristina Flaut (Ovidius University, Romania), Etibar S. Penahov (Baku State University, Azerbaijan), H. Hidayet Kosal (Sakarya University, Turkey),

Lyudmila Romakina (Saratov State University),

Mehmet Ali Gungor (Sakarya University, Turkey),

Soley Ersoy (Sakarya University, Turkey),

Wolfgang Sproessig (Technical University Freiburg, Germany).

DOI 10.2478/9788395793882-001

New versions of q-surface pencil in Euclidean 3-space Aziz Yazla1 and Muhammed T. Sariaydin2

1,2Selcuk University, Faculty of Science, Department of Mathematics, 42130, Konya, Turkey E-mail: azizyazla@gmail.com1, talatsariaydin@gmail.com2

Abstract

In this paper, the q-surface pencil is studied in Euclidean 3-space. By using q-frame in Euclidean space, Firstly, we define q-surface pencil. Then, we give the necessary and sufficient condition for a curve to be a geodesic curve and to be an asymptotic curve on a q-surface pencil. Then, we study this subject for an offset q-surface pencil.

2010 Mathematics Subject Classification. 53A05 53A04

Keywords. Geodesic Curve, Asymptotic Curve, q-Surface Pencil, Offset Surface.

1

Introduction

Geodesic on a surface corresponds to the shortest path between any two points on the surface.

When one flattens a developable surface into a planar shape without distortion, any geodesic on the surface will be mapped to a straight line in the planar shape. Therefore, a good algorithm which is needed to flatten a non-developable surface with as little distortion as possible must preserve the geodesic curvatures on the surface, [16].

A geodesic on a