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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.
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.
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.