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    The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space
    (Mdpi, 2023) Celik, Serkan; Karadag, Haci Bayram; Samanci, Hatice Kusak
    A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Mobius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature.
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    THE SHAPE OPERATOR OF THE BEZIER SURFACES IN MINKOWSKI-3 SPACE
    (Editura Bibliotheca-Bibliotheca Publ House, 2020) Samanci, Hatice Kusak; Celik, Serkan; Incesu, Muhsin
    Bezier surfaces are commonly used in Computer-Aided Geometric Design since it enables in geometric modeling of the objects. In this study, the shape operator of the timelike and spacelike surfaces has been analyzed in Minkowski-3 space. Then, the obtained results were applied to a numeric example.