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( Yasin Unluturk ),( Suha Yilmaz ),( Cumali Ekici ) 호남수학회 2019 호남수학학술지 Vol.41 No.1
In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.
Unluturk, Yasin,Yilmaz, Suha,Ekici, Cumali The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.
Yasin Unluturk,Suha Yilmaz 호남수학회 2022 호남수학학술지 Vol.44 No.1
In this study, we obtain the spherical images of minimal curves in the complex space in $\mathbb{C}^{4}$ which are obtained by translating Cartan frame vector fields to the centre of hypersphere, and present their properties such as becoming isotropic cubic, pseudo helix, and spherical involutes. Also, we examine minimal curves which are characterized by a system of differential equations.
A NEW CONSTRUCTION OF BIENERGY AND BIANGLE IN LORENTZ 5-SPACE
( Talat Korpinar ),( Yasin Unluturk ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
In this study, we firstly compute the energies and the angles of Frenet vector fields in Lorentz 5-space L<sup>5</sup>. Then we obtain the bienergies and biangels of Frenet vector fields in L<sup>5</sup> by using the values of energies and angles. Finally, we present the relations among energies, angles, bienergies, and biangles with graphics.
ISOTROPIC SMARANDACHE CURVES IN THE COMPLEX 4-SPACE
Ergut, Mahmut,Yilmaz, Suha,Unluturk, Yasin The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.1
We define the $e^{\alpha}_1e^{\alpha}_3$-isotropic Smarandache curves of type-1 and type-2, the $e^{\alpha}_1e^{\alpha}_2e^{\alpha}_3$-isotropic Smarandache curve, and the $e^{\alpha}_1e^{\alpha}_2e^{\alpha}_4$-isotropic Smarandache curves of type-1 and type-2. Then we examine these kinds of isotropic Smarandache curve according to Cartan frame in the complex 4-space $\mathbb{C}^4$ and give some differential geometric properties of these Samarandache curves.
ISOTROPIC SMARANDACHE CURVES IN THE COMPLEX 4-SPACE
( Mahmut Ergut ),( Suha Yilmaz ),( Yasin Unluturk ) 호남수학회 2018 호남수학학술지 Vol.40 No.1
We define the e1<sup>a</sup> e3<sup>a</sup> -isotropic Smarandache curves of type-1 and type-2, the e1<sup>a</sup> e2<sup>a</sup> e3<sup>a</sup> -isotropic Smarandache curve, and e1<sup>a</sup> e2<sup>a</sup> e4<sup>a</sup>-isotropic Smarandache curves of type-1 and type-2. Then we examine these kinds of isotropic Smarandache curve according to Cartan frame in the complex 4-space C<sup>4</sup> and give some differential geometric properties of these Samarandache curves.
The Evaluation of the Conditions for the Non-Null Curves to be Inextensible in Lorentzian 6-Space
Aslan, Muradiye Cimdiker,Unluturk, Yasin Department of Mathematics 2021 Kyungpook mathematical journal Vol.61 No.4
In this study, we obtain various conditions for the non-null curve flows to be inextensible in the 6-dimensional Lorentzian space 𝕃<sup>6</sup>. Then, we find partial differential equations which characterize the family of inextensible non-null curves.