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    A New Approach to Mannheim Curve in Euclidean 3-Space
    (Tamkang University, 2021) Uçum, Ali; Camcı, Çetin; İlarslan, Kazım
    In this article, a new approach is given for Mannheim curves in 3-dimensional Euclidean space. Thanks to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Mannheim curve in E3. In addition, related examples and graphs are given by showing that Salkowski and anti-Salkowski curves can be the examples of Mannheim curves and their mates. Finally, the Mannheim partner curves are characterized in E3.
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    New type of timelike (1, 3)-Bertrand curves in Minkowski space-time
    (Institute of Mathematics, 2023) Camcı, Çetin; İlarslan, Kazım; Uçum, Ali
    In the present paper, we define the notion of (1, 3)-V Bertrand curves in E41. Then we find the necessary and sufficient conditions for timelike curves in E41 to be (1, 3)-V Bertrand curves. Finally we give some related examples. © 2023, Institute of Mathematics. All rights reserved.
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    Surfaces of Osculating Circles in Euclidean Space
    (Springer, 2024) Lopez, Rafael; Camcı, Çetin; Uçum, Ali; İlarslan, Kazım
    The aim of this paper is to define a new class of surfaces in Euclidean space using the concept of osculating circle. Given a regular curve C, the surface of osculating circles generated by C is the set of all osculating circles at all points of C. It is proved that these surfaces contain a one-parametric family of planar lines of curvature. A classification of surfaces of osculating circles is given in the family of canal surfaces, Weingarten surfaces, surfaces with constant Gauss curvature and surfaces with constant mean curvature.