Mahmut Mak
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Mahmut Mak has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Hasan Altınbaş
Department of Mathematics, Kırşehir Ahi Evran University, Kırşehir 40100, Turkey
3 shared publications - Levent Kula
Department of Mathematics, Faculty of Sciences and Arts, Kırşehir Ahi Evran University, Kırşehir 40100, Türkiye
2 shared publications Baki Karlığa
Department of Mathematics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara, Turkey
1 shared publication- Bülent Altunkaya
Department of Mathematics Education Faculty of Education Kırşehir Ahi Evran University Kırşehir Turkiye
1 shared publication - Yanlin Li
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
1 shared publication
Latest Publications
- 10 October 2024
- Published by World Scientific Pub Co Pte Ltd in Asian-European Journal of Mathematics
- Vol. 18 (01)
Ac-slant curves in Euclidean 3-space
In this study, we introduce a new type of space curve which is called ac-slant curve whose inner product of its acceleration vector and a fixed direction is a constant. Then, we give a characterization according to the curvatures of ac-slant curve. Later on, we obtain relationship between an ac-slant curve and some special curves (spherical curve, helix, slant helix, Salkowski curve, rectifying curve). Similarly to concept of ac-slant curves, we consider normalized ac-slant curve which has a unit acceleration vector and give a characterization with respect to its curvatures. Especially, we give some results for ac-slant or normalized ac-slant curves with respect to the magnitude of its velocity and acceleration vector.
- 10 October 2024
- Published by World Scientific Pub Co Pte Ltd in Asian-European Journal of Mathematics
- Vol. 18 (01)
Ac-slant curves in Euclidean 3-space
In this study, we introduce a new type of space curve which is called ac-slant curve whose inner product of its acceleration vector and a fixed direction is a constant. Then, we give a characterization according to the curvatures of ac-slant curve. Later on, we obtain relationship between an ac-slant curve and some special curves (spherical curve, helix, slant helix, Salkowski curve, rectifying curve). Similarly to concept of ac-slant curves, we consider normalized ac-slant curve which has a unit acceleration vector and give a characterization with respect to its curvatures. Especially, we give some results for ac-slant or normalized ac-slant curves with respect to the magnitude of its velocity and acceleration vector.
- Open Access
- 17 August 2023
- Published by MDPI AG in Mathematics
- Vol. 11 (16) , 3571
Framed Natural Mates of Framed Curves in Euclidean 3-Space
In this study, we consider framed curves as regular or singular space curves with an adapted frame in Euclidean 3-space. We define framed natural mates of a framed curve that are tangent to the generalized principal normal of the framed curve. Subsequently, we present the relationships between a framed curve and its framed natural mates. In particular, we establish some necessary and sufficient conditions for the framed natural mates of specific framed curves, such as framed spherical curves, framed helices, framed slant helices, and framed rectifying curves. Finally, we support the concept with some examples.
- 17 August 2023
- Published by MDPI AG in Mathematics
- Vol. 11 (16) , 3571
Open AccessFramed Natural Mates of Framed Curves in Euclidean 3-Space
In this study, we consider framed curves as regular or singular space curves with an adapted frame in Euclidean 3-space. We define framed natural mates of a framed curve that are tangent to the generalized principal normal of the framed curve. Subsequently, we present the relationships between a framed curve and its framed natural mates. In particular, we establish some necessary and sufficient conditions for the framed natural mates of specific framed curves, such as framed spherical curves, framed helices, framed slant helices, and framed rectifying curves. Finally, we support the concept with some examples.
- Open Access
- 1 January 2023
- Published by National Library of Serbia in Filomat
- Vol. 37 (28) , 9627-9640
Framed clad helices in Euclidean 3-space
In this study, we introduce framed clad helices, which are a generalization of clad (i.e. C-slant or 2-slant) helices in Euclidean 3-space. They also include framed helices and framed slant helices. After, we give a characterization of the framed clad helices using the alternative adapted frame, which is more useful than the adapted frame of a framed curve. Moreover, we prove the existence of framed spherical images of any framed curve using alternative adapted frames. Additionally, we obtain interesting results regarding the relationship between a framed clad helix and its framed spherical images. Finally, we support the concept with some nice graphics.
- 1 January 2023
- Published by National Library of Serbia in Filomat
- Vol. 37 (28) , 9627-9640
Open AccessFramed clad helices in Euclidean 3-space
In this study, we introduce framed clad helices, which are a generalization of clad (i.e. C-slant or 2-slant) helices in Euclidean 3-space. They also include framed helices and framed slant helices. After, we give a characterization of the framed clad helices using the alternative adapted frame, which is more useful than the adapted frame of a framed curve. Moreover, we prove the existence of framed spherical images of any framed curve using alternative adapted frames. Additionally, we obtain interesting results regarding the relationship between a framed clad helix and its framed spherical images. Finally, we support the concept with some nice graphics.
- Open Access
- 1 October 2022
- Published by Hacettepe University in Hacettepe Journal of Mathematics and Statistics
- Vol. 51 (5) , 1333-1347
Mappings that transform helices from Euclidean space to Minkowski space
In this study, we introduce mappings that transform helices in Euclidean $ n $-space to non-null helices in Minkowski $ n $-space or Minkowski $ (n+1) $-space. Furthermore, we show that these mappings preserve the axes of the helices, and we also obtain the invariants of the mappings. Especially, by using these mappings, we give some examples of non-null helices which are constructed in Minkowski 3-space or Minkowski 4-space from some helices in Euclidean 3-space.- 1 October 2022
- Published by Hacettepe University in Hacettepe Journal of Mathematics and Statistics
- Vol. 51 (5) , 1333-1347
Open AccessMappings that transform helices from Euclidean space to Minkowski space
In this study, we introduce mappings that transform helices in Euclidean $ n $-space to non-null helices in Minkowski $ n $-space or Minkowski $ (n+1) $-space. Furthermore, we show that these mappings preserve the axes of the helices, and we also obtain the invariants of the mappings. Especially, by using these mappings, we give some examples of non-null helices which are constructed in Minkowski 3-space or Minkowski 4-space from some helices in Euclidean 3-space. - Open Access
- 30 June 2021
- Published by Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics in Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
- Vol. 70 (1) , 522-540
Natural and conjugate mates of Frenet curves in three-dimensional Lie group
In this study, we introduce the natural mate and conjugate mate of a Frenet curve in a three dimensional Lie group $ \mathbb{G} $ with bi-invariant metric. Also, we give some relationships between a Frenet curve and its natural mate or its conjugate mate in $ \mathbb{G} $. Especially, we obtain some results for the natural mate and the conjugate mate of a Frenet curve in $ \mathbb{G} $ when the Frenet curve is a general helix, a slant helix, a spherical curve, a rectifying curve, a Salkowski (constant curvature and non-constant torsion), anti-Salkowski (non-constant curvature and constant torsion), Bertrand curve. Finally, we give nice graphics with numeric solution in Euclidean 3-space as a commutative Lie group.- 30 June 2021
- Published by Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics in Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
- Vol. 70 (1) , 522-540
Open AccessNatural and conjugate mates of Frenet curves in three-dimensional Lie group
In this study, we introduce the natural mate and conjugate mate of a Frenet curve in a three dimensional Lie group $ \mathbb{G} $ with bi-invariant metric. Also, we give some relationships between a Frenet curve and its natural mate or its conjugate mate in $ \mathbb{G} $. Especially, we obtain some results for the natural mate and the conjugate mate of a Frenet curve in $ \mathbb{G} $ when the Frenet curve is a general helix, a slant helix, a spherical curve, a rectifying curve, a Salkowski (constant curvature and non-constant torsion), anti-Salkowski (non-constant curvature and constant torsion), Bertrand curve. Finally, we give nice graphics with numeric solution in Euclidean 3-space as a commutative Lie group. - Open Access
- 25 June 2020
- Published by Cumhuriyet University in Cumhuriyet Science Journal
- Vol. 41 (2) , 327-343
Some characterizations of timelike rectifying curves in de sitter 3 space
De Sitter space is a non-flat Lorentzian space form with positive constant curvature which plays an important role in the theory of relativity. In this paper, we define the notions of timelike rectifying curve and timelike conical surface in De Sitter 3-space as Lorentzian viewpoint. Moreover, we give some nice characterizations and results of a timelike rectifying curves with respect to curve-hypersurface frame in De Sitter 3-space which is a three dimensional pseudo-sphere in Minkowski 4-space.
- 25 June 2020
- Published by Cumhuriyet University in Cumhuriyet Science Journal
- Vol. 41 (2) , 327-343
Open AccessSome characterizations of timelike rectifying curves in de sitter 3 space
De Sitter space is a non-flat Lorentzian space form with positive constant curvature which plays an important role in the theory of relativity. In this paper, we define the notions of timelike rectifying curve and timelike conical surface in De Sitter 3-space as Lorentzian viewpoint. Moreover, we give some nice characterizations and results of a timelike rectifying curves with respect to curve-hypersurface frame in De Sitter 3-space which is a three dimensional pseudo-sphere in Minkowski 4-space.
- Open Access
Some Characterizations of Timelike Rectifying Curves in De Sitter 3-Space
De Sitter space is a non-flat Lorentzian space form with positive constant curvature which plays an important role in the theory of relativity. In this paper, we define the notions of timelike rectifying curve and timelike conical surface in De Sitter 3-space as Lorentzian viewpoint. Moreover, we give some nice characterizations and results of a timelike rectifying curves with respect to curve-hypersurface frame in De Sitter 3-space which is a three dimensional pseudo-sphere in Minkowski 4-space.
Open AccessSome Characterizations of Timelike Rectifying Curves in De Sitter 3-Space
De Sitter space is a non-flat Lorentzian space form with positive constant curvature which plays an important role in the theory of relativity. In this paper, we define the notions of timelike rectifying curve and timelike conical surface in De Sitter 3-space as Lorentzian viewpoint. Moreover, we give some nice characterizations and results of a timelike rectifying curves with respect to curve-hypersurface frame in De Sitter 3-space which is a three dimensional pseudo-sphere in Minkowski 4-space.
- Open Access
- 30 October 2017
- Published by Mathematical Sciences and Applications E-Notes in Mathematical Sciences and Applications E-Notes
- Vol. 5 (2) , 89-97
Some Special Associated Curves of Non-degenerate Curve in Anti de Sitter 3-Space
Frenet curve, associated curve, direction curve, donor curve, helix,
- 30 October 2017
- Published by Mathematical Sciences and Applications E-Notes in Mathematical Sciences and Applications E-Notes
- Vol. 5 (2) , 89-97
Open AccessSome Special Associated Curves of Non-degenerate Curve in Anti de Sitter 3-Space
Frenet curve, associated curve, direction curve, donor curve, helix,
- Open Access
- 20 November 2014
- Published by Wiley in Journal of Applied Mathematics
- Vol. 2014, 1-12
Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space
We consider hyperbolic rotation (), hyperbolic translation (), and horocyclic rotation () groups in, which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups ofin. Also, we give explicit parametrization of these invariant surfaces with respect to constant hyperbolic curvature of profile curves. Finally, we obtain some corollaries for flat and minimal invariant surfaces which are associated with de Sitter and hyperbolic shape operator in.- 20 November 2014
- Published by Wiley in Journal of Applied Mathematics
- Vol. 2014, 1-12
Open AccessInvariant Surfaces under Hyperbolic Translations in Hyperbolic Space
We consider hyperbolic rotation (), hyperbolic translation (), and horocyclic rotation () groups in, which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups ofin. Also, we give explicit parametrization of these invariant surfaces with respect to constant hyperbolic curvature of profile curves. Finally, we obtain some corollaries for flat and minimal invariant surfaces which are associated with de Sitter and hyperbolic shape operator in.