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TRANS-SASAKIAN MANIFOLDS WITH RESPECT TO GENERALIZED TANAKA-WEBSTER CONNECTION
( Ahmet Kazan ),( H. Bayram Karadag ) 호남수학회 2018 호남수학학술지 Vol.40 No.3
In this study, we use the generalized Tanaka-Webster connection on a trans-Sasakian manifold of type (α, β) 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.
TRANS-SASAKIAN MANIFOLDS WITH RESPECT TO GENERALIZED TANAKA-WEBSTER CONNECTION
Kazan, Ahmet,Karadag, H.Bayram The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.3
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.
LAPLACE-BELTRAMI MINIMALITY OF TRANSLATION HYPERSURFACES IN E<sup>4</sup>
( Ahmet Kazan ),( Mustafa Altin ) 호남수학회 2023 호남수학학술지 Vol.45 No.2
In the present paper, we study translation hypersurfaces in E<sup>4</sup>. In this context, firstly we obtain first, second and third Laplace- Beltrami (LB<sup>I</sup>, LB<sup>II</sup> and LB<sup>III</sup>) operators of the translation hypersurfaces in E<sup>4</sup>. By solving second and third order nonlinear ordinary differential equations, we prove theorems that contain LB<sup>I</sup>-minimal, LB<sup>II</sup>-minimal and LB<sup>III</sup>-minimal translation hypersurfaces in E<sup>4</sup>.
RULED SURFACES IN E<sup>3</sup> WITH DENSITY
Altin, Mustafa,Kazan, Ahmet,Karadag, H.Bayram The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.4
In the present paper, we study curves in 𝔼<sup>3</sup> with density $e^{ax^2+by^2}$, where a, b ∈ 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.
Ruled surfaces in $E^{3}$ with density
Mustafa Altin,Ahmet Kazan,H.Bayram Karadag 호남수학회 2019 호남수학학술지 Vol.41 No.4
In the present paper, we study curves in $\mathbb{E}^{3}$ with density $e^{ax^{2}+by^{2}},$ where $a,b\in \mathbb{R}$ 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.
RULED SURFACES IN E<sup>3</sup> WITH DENSITY
( Mustafa Altin ),( Ahmet Kazan ),( H. Bayram Karadag ) 호남수학회 2019 호남수학학술지 Vol.41 No.4
In the present paper, we study curves in E<sup>3</sup> with den- sity e<sup>ax2+by2 </sup>, where a, b ∈ R not all zero constants and give the parametric expressions of the curves with vanishing weighted cur- vature. 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 characteriza- tions about these ruled surfaces by obtaining the mean curvatures, Gaussian curvatures, distribution parameters and striction curves of them.
CANAL HYPERSURFACES GENERATED BY NON-NULL CURVES IN LORENTZ-MINKOWSKI 4-SPACE
Mustafa Altın,Ahmet Kazan,윤대원 대한수학회 2023 대한수학회보 Vol.60 No.5
In the present paper, firstly we obtain the general expression of the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres, pseudo hyperbolic hyperspheres and null hypercones whose centers lie on a non-null curve with non-null Frenet vector fields in $E_{1} ^{4}$ and give their some geometric invariants such as unit normal vector fields, Gaussian curvatures, mean curvatures and principal curvatures. Also, we give some results about their flatness and minimality conditions and Weingarten canal hypersurfaces. Also, we obtain these characterizations for tubular hypersurfaces in $E_{1}^{4}$ by taking constant radius function and finally, we construct some examples and visualize them with the aid of Mathematica.