Yazar "Kazan, Ahmet" seçeneğine göre listele

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    Embankment Surfaces in Euclidean 3-Space and Their Visualizations
    (Rgn Publ, 2019) Kazan, Ahmet; Karadag, H. Bayram
    In 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.
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    Helix Surfaces in Euclidean 3-Space with Density
    (2021) Kazan, Ahmet; Kazan, Sema
    The 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.
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    HYPERSURFACE FAMILIES WITH SMARANDACHE CURVES IN GALILEAN 4-SPACE
    (Ankara Univ, Fac Sci, 2021) Altin, Mustafa; Kazan, Ahmet; Karadag, H. Bayram
    In this paper, we study the hypersurface families with Smarandache curves in 4-dimensional Galilean space G(4) and give the conditions for different Smarandache curves to be parameter and the curve which generates the Smarandache curves is geodesic on a hypersurface in G(4): Also, we investigate three types of marching-scale functions for one of these hypersurfaces and construct an example for it.
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    LOCALLY DECOMPOSABLE GOLDEN RIEMANNIAN TANGENT BUNDLES WITH CHEEGER-GROMOLL METRIC
    (Univ Miskolc Inst Math, 2016) Kazan, Ahmet; Karadag, H. Bayram
    In this paper we obtain a condition for the tangent bundle (TM, (J) over tilde, (g) over tilde) to be locally decomposable Golden Riemannian tangent bundle, where (J) over tilde is the Golden structure on TM and (g) over tilde is the Cheeger-Gromoll metric.
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    MAGNETIC NON-NULL CURVES ACCORDING TO PARALLEL TRANSPORT FRAME IN MINKOWSKI 3-SPACE
    (Ankara Univ, Fac Sci, 2018) Kazan, Ahmet; Karadag, H. Bayram
    In this study, we define the notions of T-magnetic, N-1-magnetic and N-2-magnetic timelike and spacelike curves in Minkowski 3-space. We obtain the magnetic vector field V when the timelike or spacelike curve is a T-magnetic, N-1-magnetic or N-2-magnetic trajectory of V and give some examples for these magnetic curves.
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    Minkowski 3-uzayında eğriler ve yüzeylerin geometrisi
    (İnönü Üniversitesi, 2011) Kazan, Ahmet
    Dört bölümden oluşan bu tezin giris bölümünde konuyla ilgili bazı genel değerlendirmeler yapılmış ve bu konuya temel olan bazı çalışmalara yer verilmiştir. İkinci bölümde, daha sonraki bölümlerde kullanılacak olan bazı temel kavramlar verilmiştir. Üçüncü bölümde, ilk olarak E31 Minkowski 3-uzayında eğrilerin genel yapıları incelenmiş, eğrilerin farklı causal karakterleri için Frenet denklemleri elde edilmiş ve bu denklemler yardımıyla eğrilerin eğrilik ve burulmaları incelenmiştir. Sonra E31 de sabit eğrilikli düzlemsel eğriler ele alınmıştır. Ayrıca yine bu uzayda helisler ve Bertrand eğrilerle ilgili bazı karakterizasyonlar verilmiştir. Bu bölümde son olarak da spacelike, timelike ve null normal eğrilere yer verilmiştir. Dördüncü bölümde önce spacelike ve timelike yüzey kavramları tanıtılmış ve ardından bu yüzeyler için ortalama eğrilik ve Gauss eğriliği lokal olarak ifade edilmiştir. Ayrıca E31 in umbilik yüzeyleri karakterize edilmiştir. Daha sonra, Minkowski 3-uzayında dönel yüzeyler genel olarak tanıtılmış ve bu yüzeyler için bazı sınıflandırmalar verilmiştir. Son olarak da regle yüzeylerin genel yapısı ve timelike regle yüzeyler için bazı karakterizasyonlar verilmiştir.
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    Monge Hypersurfaces in Euclidean 4-Space with Density
    (Gazi Univ, 2020) Altin, Mustafa; Kazan, Ahmet; Karadag, H. Bayram
    In 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 E-4 with different densities. In this context, we obtain the weighted minimal and weighted flat Monge hypersurfaces in E-4 with densities e(alpha x+beta y+yz+mu r)(linear density) and e(alpha x2+beta y2+yz2+mu t2) with the aid of different choices of constants alpha,beta,gamma and mu, where alpha,beta,gamma and mu are not all zero constants.
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    Nonnull Curves with Constant Weighted Curvature in Lorentz-Minkowski Plane with Density
    (2020) Altın, Mustafa; Kazan, Ahmet; Karadağ, Hacı Bayram
    Nonnull Curves with Constant Weighted Curvature in Lorentz-Minkowski Plane with Density Abstract: In this paper, the parametric expressions of spacelike and timelike curves with constant weighted curvature for some cases of a and b in Lorentz-Minkowski plane with density e ax+by are obtained.
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    Paracontact Tangent Bundles with Cheeger-Gromoll Metric
    (Springer Basel Ag, 2015) Kazan, Ahmet; Karadag, H. Bayram
    In this paper, we define the almost paracontact metric structure on a tangent bundle TM with Cheeger-Gromoll (C-G) metric and obtain the normality condition for it. We define the paracontact C-G metric tangent bundle, K-paracontact C-G metric tangent bundle and C-G para-Sasakian tangent bundle and give some characterizations about them. Also, we give the Riemannian curvature tensor RI integral and the sectional curvature KI integral of the almost paracontact C-G metric tangent bundle TM. Finally, we obtain the Ricci curvature SI integral and the scalar curvature of the almost paracontact C-G metric tangent bundle TM with the aid of the orthonormal basis of TM.
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    Paracontact Tangent Bundles with Cheeger-Gromoll Metric (vol 12, pg 497, 2015)
    (Springer Basel Ag, 2016) Kazan, Ahmet; Karadag, H. Bayram
    [Abstract Not Available]
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    Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves
    (2019) Gündüz, Hakan; Kazan, Ahmet; Karadağ, Hacı Bayram
    Abstract: To 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.
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    ROTATIONAL SURFACES GENERATED BY PLANAR CURVES IN E3 WITH DENSITY
    (Etamaths Publ, 2019) Altin, Mustafa; Kazan, Ahmet; Karadag, H. Bayram
    In 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.
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    Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in (L 3 , ax2 + by2 )
    (2020) Altın, Mustafa; Kazan, Ahmet; Karadağ, H. Bayram
    In this study, firstly we give the weighted curvatures of non-null planar curves in Lorentz-Minkowski space with density eax2+by2and obtain the planar curves whose weighted curvaturesvanish in this space under the condition that the constants a and b are not zero at the same time.After giving the Frenet vectors of the non-null planar curves with zero weighted curvature inLorentz-Minkowski space with density eax2, we create the Smarandache curves of them. With theaid of these curves and their Smarandache curves, we get the ruled surfaces whose base curvesare non-null curves of which vanishing weighted curvature and ruling curves are Smarandachecurves of them. Followingly, we give some characterizations for these ruled surfaces by obtainingthe 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 curvaturesin Lorentz-Minkowski space E31 with density eax2+by2are studied under the condition that theconstants a and b are not zero at the same time. We draw the graphics of the obtained surfaces.
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    Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in (L3, ax2
    (Int Electronic Journal Geometry, 2020) Altin, Mustafa; Kazan, Ahmet; Karada, H. Bayram
    In this study, firstly we give the weighted curvatures of non-null planar curves in Lorentz-Minkowski space with density eax(2)+by(2) and obtain the planar curves whose weighted curvatures vanish in this space under the condition that the constants a and b are not zero at the same time. After giving the Frenet vectors of the non-null planar curves with zero weighted curvature in Lorentz-Minkowski space with density eax(2), 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 of which 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-1(3) with density eax(2) +by(2) are studied under the condition that the constants a and b are not zero at the same time. We draw the graphics of the obtained surfaces.
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    RULED SURFACES IN E3 WITH DENSITY
    (Honam Mathematical Soc, 2019) Altin, Mustafa; Kazan, Ahmet; Karadag, H. Bayram
    In 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.
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    Tanjant demetler üzerinde cheeger-gromoll metrikli bazı yapılar
    (İnönü Üniversitesi, 2015) Kazan, Ahmet
    Beş bölümden oluşan bu tezin giriş bölümünde konuyla ilgili bazı genel değerlendirmeler yapılmış ve bu konuya temel olan bazı çalışmalara yer verilmiştir. İkinci bölümde, tezin orijinal bölümlerinde kullanılacak olan bazı temel kavramlar sunulmuştur. Üçüncü bölümde öncelikle tanjant demetler üzerinde doğal metrik kavramı tanımlanarak bazı sonuçlar verilmiş ve ardından da tanjant demetler üzerinde doğal metrik türlerinden biri olan Cheeger-Gromoll (C-G) metrik tanımlanarak bu metrikle ilgili bazı geometrik sonuçlar verilmiştir. Tezin dördüncü ve beşinci bölümleri orijinal çalışmalardan oluşmakta olup, dördüncü bölümde ilk olarak C-G metrikli hemen hemen parakontakt tanjant demetler tanımlanmış ve bu tanjant demetlerin normalliğini karakterize eden teorem ifade edilmiştir. Ayrıca, C-G metrikli parakontakt, K-parakontakt ve para-Sasakian tanjant demetler tanımlanarak bu kavramlarla ilgili bazı sonuçlar elde edilmiştir. Bu bölümde son olarak da, C-G metrikli hemen hemen parakontakt tanjant demetlerin eğrilikleri ile ilgili bazı sonuçlar verilmiştir. Beşinci ve son bölümde ise, ilk önce bir M manifoldu üzerinde metalik yapı kavramı ifade edilerek TM tanjant demeti üzerinde TM metalik yapı kavramı tanımlanmıştır. Daha sonra C-G metrikle donatılmış bir metalik tanjant demetin metalik Riemannian tanjant demet olma şartı elde edilmiştir. Son olarak da, C-G metrikle donatılmış metalik Riemannian tanjant demetlerin bir sınıfı olan Golden Riemannian tanjant demetlerin lokal olarak ayrıştırılabilir olmasıyla ilgili bir teorem verilmiştir.
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    TRANS-SASAKIAN MANIFOLDS WITH RESPECT TO GENERALIZED TANAKA-WEBSTER CONNECTION
    (Honam Mathematical Soc, 2018) Kazan, Ahmet; Karadag, H. Bayram
    In this study, we use the generalized Tanaka-Webster connection on a trans-Sasakian manifold of type (alpha, beta) and obtain the curvature tensors of a trans-Sasakian manifold with respect to this connection. Also, we investigate some special curvature conditions of a trans-Sasakian manifold with respect to generalized Tanaka-Webster connection and finally, give an example for trans-Sasakian manifolds.
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    WEIGHTED MINIMAL AND WEIGHTED FLAT SURFACES OF REVOLUTION IN GALILEAN 3-SPACE WITH DENSITY
    (Etamaths Publ, 2018) Kazan, Ahmet; Karadag, H. Bayram
    In this paper, we obtain the weighted mean and weighted Gaussian curvatures of surfaces of revolution in Galilean 3-space with density e(a1x2+a2y2+a3z2), a(1), a(3), a(3) is an element of R not all zero. Also, we investigate some cases of weighted minimal surfaces of revolution according to a(i), i = 1, 2, 3 and weighted flat surfaces of revolution.