Yazar "Kazan, Ahmet" seçeneğine göre listele
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Öğe Conformally-projectively flat trans-Sasakian statistical manifolds(Elsevier, 2019) Kazan, AhmetIn this study, the notion of trans-Sasakian statistical manifold is defined, some results for this manifold's curvature tensors are given, an example of 3-dimensional trans-Sasakian statistical manifold is constructed and some characterizations about ?-conformal-projective flatness of a trans-Sasakian statistical manifold are given.Öğe e^(ax+by) Yoğunluklu E^3_1 Uzayında Sıfır Ağırlıklı Eğriliğe Sahip Null Olmayan Düzlemsel Eğrilerin Oluşturduğu Yüzeyler(Erzincan Üniversitesi, 2020) Altın, Mustafa; Kazan, AhmetBu çalışmada, ... yoğunluklu ... 1 3 Lorentz-Minkowski uzayında, ikisi aynı anda sıfır olmayan ... ve ... sabitlerinin durumlarına göre, ağırlıklı eğrilikleri sıfır olan spacelike ve timelike düzlemsel eğriler yardımıyla oluşturulan dönel yüzeyler ve regle yüzeyler çalışılmıştır.Öğe Embankment Surfaces in Euclidean 3-Space and Their Visualizations(Communications in Mathematics and Applications, 2019) Kazan, Ahmet; Karadağ, Hacı BayramIn the present paper, we obtain the parametric representation of an embankment surface and give an example for it. We define the notions of embankmentlike surfaces and tubembankmentlike surfaces. Furthermore, we create some embankmentlike and tubembankmentlike surface examples with the aid of different directrix and draw these directrix and surfaces. Also, we find the Gaussian, mean and second Gaussian curvatures of these surfaces and draw the Gaussian, mean and second Gaussian curvature functions' graphics and the variations of Gaussian, mean and second Gaussian curvatures on related surfaces with the aid of Mathematica.Öğe Helix Surfaces in Euclidean 3-Space with Density(Osman SAĞDIÇ, 2021) Kazan, Ahmet; Kazan, SemaThe differential geometry of helix curves and helix hypersurfaces in different spaces has important application areas in many disciplines. Also, the notion of weighted manifold is become to be a very popular topic for scientists in recent years. In this context, after defining the notions of weighted mean curvature (or...-mean curvature) and weighted Gaussian curvature (or ...-Gaussian curvature) of an n-dimensional hypersurface on manifolds with density, lots of studies have been done by differential geometers in different spaces with different densities. So, in the present study, firstly we give the normal vector field, mean curvature and Gaussian curvature of a helix surface in three dimensional Euclidean space and after that, we obtain the weighted mean curvature and weighted Gaussian curvature of a helix surface generated by a unit speed planar curve in three dimensional Euclidean space with different three densities by stating the parametric equation of this surface. However, we know that a hypersurface is weighted minimal and weighted flat in Eucilidean 3-space with density if the weighted mean curvature and the weighted Gaussian curvature vanish, respectively. So, by using these definitions, we obtain the weighted minimal helix surfaces for these different densities and give some results for weighted flatness of the helix surfaces in Euclidean 3-space. We hope that, this study will bring a new viewpoint to differential geometers who are dealing with constant angle surfaces and in near future, one can handle these surfaces in different spaces with another densities.Öğe Monge hypersurfaces in euclidean 4-space with density(Gazi Üniversitesi, 2020) Altın, Mustafa; Kazan, Ahmet; Karadağ, Hacı BayramIn the present study, firstly we give the mean and Gaussian curvatures of a Monge hypersurface in 4-dimensional Euclidean space. After this, we study on Monge hypersurfaces in with different densities. In this context, we obtain the weighted minimal and weighted flat Monge hypersurfaces in with densities (linear density) and with the aid of different choices of constants and , where and are not all zero constants.Öğe Rotational hypersurfaces in Lorentz-Minkowski 4-space(Hacettepe Üniversitesi, 2021) Altın, Mustafa; Kazan, AhmetIn this study, we study rotational hypersurfaces in 4-dimensional Lorentz-Minkowski space. We find the rotational hypersurfaces about spacelike axis according to Gaussian and mean curvatures in E-1(4) and give some results with the aid of the Gaussian and mean curvatures. After that, we deal with the Gauss map of rotational hypersurface about spacelike axis by obtaining the Gaussian and mean curvatures. We obtain the second and third Laplace-Beltrami operators on rotational hypersurface about spacelike axis in E-1(4) . Also, we give these characterizations for rotational hypersurfaces about timelike and lightlike axes, too.Öğe Rotational surfaces generated by cubic hermitian and cubic bezier curves(Gazi Üniversitesi, 2019) Gündüz, Hakan; Kazan, Ahmet; Karadağ, Hacı BayramTo tackle the geometric design in adjusting shapes of rotation surfaces, firstly the rotation surfaces have been constructed by using cubic Hermitian and cubic Bezier curves with two local shape parameters. It has been seen that, the new rotational surfaces which have been constructed have a good performance on adjusting their shapes by changing the local shape parameters. Also, the rotational surfaces generated by cubic Hermitian and cubic Bezier curves have provided a valuable way for the design of interesting surfaces. In this context, some characterizations have been given for these rotational surfaces obtaining the mean and Gaussian curvatures of them.Öğe Rotational surfaces generated by planar curves in E3 with density(Etamaths Publishing, 2019) Altın, Mustafa; Kazan, Ahmet; Karadağ, Hacı BayramIn this paper, we obtain the parametric expressions of curves which have zero weighted curvature in a plane with density e(ax+by) and create the Smarandache curves of the obtaining curves. Also, we construct the rotational surfaces which are generated by planar curves with vanishing weighted curvature and give some characterizations for them.Öğe Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in (L 3 , ax2 + by2 )(Kazım İlarslan, 2020) Altın, Mustafa; Kazan, Ahmet; Karadağ, Hacı BayramIn this study, firstly we give the weighted curvatures of non-null planar curves in Lorentz-Minkowski space with density e^(ax2+by2) and we obtain the planar curves whose weighted curvatures vanish in this space according to the cases of not all zero constants a and b. After giving the Frenet vectors of the non-null planar curves with zero weighted curvature in Lorentz-Minkowski space with density e^(ax2), we create the Smarandache curves of them. With the aid of these curves and their Smarandache curves, we get the ruled surfaces whose base curves are non-null curves with vanishing weighted curvature and ruling curves are Smarandache curves of them. Followingly, we give some characterizations for these ruled surfaces by obtaining the mean and Gaussian curvatures, distribution parameters and striction curves of them. Also, rotational surfaces which are generated by non-null planar curves with zero weighted curvatures in Lorentz-Minkowski space E^3_1 with density e^(ax2+by2) are studied according to some cases of not all zero constants a and b. We draw the graphics of obtained surfaces.Öğe Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density(Celal Bayar Üniversitesi, 2020) Altın, Mustafa; Kazan, Ahmet; Karadağ, H.BayramIn the present study, firstly we recall the parametric expressions of planar curves with zero ...-curvature in Euclidean 3-space with density ... 1 and with the aid of the Frenet frame of these planar curves, we obtain the Smarandache curves of them. After that, we study on ruled surfaces which are constructed by the curves with zero ...-curvature in Euclidean 3-space with density ...1 and their Smarandache curves by giving the striction curves, distribution parameters, mean curvature and Gaussian curvature of these ruled surfaces. Also, we give some examples for these surfaces by plotting their graphs. We use Mathematica when we are plotting the graphs of examples.Öğe Ruled surfaces in E 3 with density(The Honam Mathematical Society (HMSK), 2019) Altın, Mustafa; Kazan, Ahmet; Karadağ, Hacı BayramIn the present paper, we study curves in E-3 with density e(,)(ax2 + by2) where a, b is an element of R not all zero constants and give the parametric expressions of the curves with vanishing weighted curvature. Also, we create ruled surfaces whose base curves are the curve with vanishing weighted curvature and the ruling curves are Smarandache curves of this curve. Then, we give some characterizations about these ruled surfaces by obtaining the mean curvatures, Gaussian curvatures, distribution parameters and striction curves of them.
