İlgi alanları

• MakaleAçık Erişim2026/r/gumushane/10407
  Canal Hypersurfaces Generated by Pseudo-Null Curves with Bishop Frame in Lorentz-Minkowski 4-Space

  Kazan, Ahmet; Kazan, Sema; Gur Mazlum, Sumeyye; Karaca, Emel; Altin, Mustafa; Grilli, Luca

  In this paper, we deal with the canal hypersurfaces that are formed as the envelope of a family of pseudo-hyperspheres or pseudo-hyperbolic hyperspheres with centers lying on a pseudo-null curve with Bishop vector fields in four-dimensional Lorentz-Minkowski space. We give main theorems which contain the parametric expressions of these canal hypersurfaces along with their Gaussian, mean, and principal curvatures and important geometric characterizations. We also provide these characterizations for tubular hypersurfaces. Finally, we construct an example to allow for better understanding and comprehension of the results.

  İncele
• MakaleYalnız künye2025/r/gumushane/11655
  Ruled surfaces generated by Darboux and instantaneous Pfaff vectors of Salkowski curves in Euclidean 3-space

  Mazlum, Sumeyye Gur; Haliscelik, Ebru Cakil; Bektas, Ozcan

  In the present study ruled surfaces generated by Darboux and instantaneous Pfaff vectors of Salkowski curves in Euclidean 3-space are considered. Some geometric properties of these surfaces such as striction curves, surface normal vectors, tangent and asymptotic planes, distribution parameters, Gaussian and mean curvatures and fundamental forms are investigated. Some results and interpretations of these surfaces are obtained.

  İncele
• MakaleAçık Erişim2024/r/gumushane/20139
  On Bishop Frames of Any Regular Curve in Euclidean 3-Space

  Mazlum, Sümeyye Gür

  Relationships between type-1 Bishop and Frenet, type-2 Bishop and Frenet, alternative and Frenet, N-Bishop and alternative frames of any regular curve in Euclidean 3-space are known. In this study, relationships between N-Bishop and Frenet frames and relationships between type-1 Bishop, type-2 Bishop and N-Bishop frames of any regular curve in Euclidean 3-space are given. In addition, pole vectors (unit vectors in the direction of Darboux vectors) belonging to these frames are computed. Last, pole and Darboux vectors belonging to these frames are compared with each other.

  İncele
• MakaleAçık Erişim2024/r/gumushane/20117
  Bishop Frames of Salkowski Curves in E3

  Mazlum, Sümeyye Gür

  In this study, alternative, type-1 Bishop, type-2 Bishop and N-Bishop frames of Salkowski curves in E3 are calculated. Moreover, curvatures, Darboux and pol vectors of these frames are found. Also, relationships between the Bishop frames, Darboux vectors and pole vectors are given.

  İncele
• MakaleAçık Erişim2024/r/gumushane/20046
  Some Applications on Spherical Indicatrices of the Helix Curve

  Şenyurt, Süleyman; Mazlum, Sümeyye Gür

  In this study, the Frenet elements of the curves that are drawn on the unit sphere by the unit vectors obtained from linear combinations of Frenet vectors of the helix curve are calculated. Moreover, Sabban frames of these curves are created and Smarandache curves are defined. Finally, the geodesic curvatures of each Smarandache curve are calculated.

  İncele
• MakaleYalnız künye2024/r/gumushane/14357
  RULED SURFACES GENERATED BY SALKOWSKI CURVE AND ITS FRENET VECTORS IN EUCLIDEAN 3-SPACE

  Çakıl, Ebru; Mazlum, Sümeyye Gür

  In present study, we introduce ruled surfaces whose base curve is the Salkowski curve in Euclidean 3-space and whose generating lines consist of the Frenet vectors of this curve (tangent, principal normal and binormal vectors). Then, we produce regular surfaces from a vector with real coefficients, which is a linear com-bination of these vectors, and we examine some special cases for these surfaces. Moreover, we present some geometric properties and graphics of all these surfaces.

  İncele
• MakaleYalnız künye2023/r/gumushane/16050
  (k, m)-TYPE SLANT HELICES FOR THE NULL CARTAN CURVE WITH THE BISHOP FRAME IN E41

  Mazlum, Sumeyye Gur; Bektas, Mehmet

  In this paper, we obtain (k, m)-type slant helices for a null Cartan curve with the Bishop frame in Minkowski space E41 .

  İncele
• MakaleYalnız künye2023/r/gumushane/16672
  ON THE SPHERICAL INDICATRIX CURVES OF THE SPACELIKE SALKOWSKI CURVE WITH TIMELIKE PRINCIPAL NORMAL IN LORENTZIAN 3-SPACE

  Aksan, Birkan; Mazlum, Sumeyye Gur

  In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths, geodesic curvatures according to the Lorentzian 3-space R31, Lorentzian sphere S21 and hyperbolic sphere H2 0 of the spherical indicatrix curves of the spacelike Salkowski curve with the timelike principal normal in R3 1 and draw the graphs of these indicatrix curves on the spheres.

  İncele
• MakaleAçık Erişim2023/r/gumushane/20316
  On Darboux Frames of Indicatrices of Spacelike Salkowski Curve with Spacelike Binormal in E13

  Mazlum, Sümeyye Gür; Aksan, Birkan

  The aim of this study is to examine Darboux frames and some other geometric properties (geodesic curvatures, geodesic torsions, normal curvatures, Darboux derivative formulas, Darboux vectors, angles, etc.) of the spherical indicatrices on Lorentzian unit sphere S_1^2 and hyperbolic unit sphere H_0^2 of the spacelike Salkowski curve with spacelike binormal in Lorentzian 3-space E_1^3. In this context, new and interesting results have been obtained for this curve. Thus, relationships between the newly obtained curvatures and torsions and the curvature and torsion of the original curve are given. Moreover, the matrix relationship between the Darboux and Frenet frames of these indicatrices is shown. Finally, the Darboux vectors belong to the Darboux frames and the Darboux vectors belong to the Frenet frames of these curves are compared.

  İncele
• MakaleYalnız künye2023/r/gumushane/14572
  Some special Smarandache ruled surfaces according to alternative frame in E3

  Senyurt, Suleyman; Mazlum, Sumeyye Gur; Canli, Davut; Can, Elif

  In this study ruled surfaces formed by alternative unit vectors that draw these curves along Smarandache curves obtained from alternative vectors and alternative unit Darboux vectors of a differentiable curve are defined. Then the Gaussian and mean curvatures of each ruled surface are computed. It is also examined whether the surfaces are developable or minimal. Finally, examples of these surfaces are given and their graphics are drawn.

  İncele