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QUATERNIONS AND HOMOTHETIC MOTIONS IN EUCLIDEAN AND LORENTZIAN SPACES
( Gülsüm Yüca ),( Yusuf Yayli ) 호남수학회 2023 호남수학학술지 Vol.45 No.2
In the present paper, we investigate homothetic motions determined by quaternions, which is a general form of our previous paper [20]. We introduce a transition between homothetic motions in 3D and 4D Euclidean and Lorentzian spaces. In other words, we give a new method that works as a handy tool for obtaining Lorentzian homothetic motions from Euclidean homothetic motions. Moreover, some remarkable properties of homothetic motions, which are given in former studies on this subject, are also examined by dual transformations. Then, we present applications and visualize them with 3D-plots. Finally, we investigate homothetic motions in dual spaces because of the importance in many fields related to kinematics.
SPLIT QUATERNIONS AND ROTATIONS IN SEMI EUCLIDEAN SPACE E<sup>4</sup><sub>2</sub>
Kula, Levent,Yayli, Yusuf Korean Mathematical Society 2007 대한수학회지 Vol.44 No.6
We review the algebraic structure of $\mathbb{H}{\sharp}$ and show that $\mathbb{H}{\sharp}$ has a scalar product that allows as to identify it with semi Euclidean ${\mathbb{E}}^4_2$. We show that a pair q and p of unit split quaternions in $\mathbb{H}{\sharp}$ determines a rotation $R_{qp}:\mathbb{H}{\sharp}{\rightarrow}\mathbb{H}{\sharp}$. Moreover, we prove that $R_{qp}$ is a product of rotations in a pair of orthogonal planes in ${\mathbb{E}}^4_2$. To do that we call upon one tool from the theory of second ordinary differential equations.
Aksoyak, Ferdag Kahraman,Yayli, Yusuf Korean Mathematical Society 2014 대한수학회보 Vol.51 No.6
In this paper, we study spacelike rotational surfaces which are called boost invariant surfaces in Minkowski 4-space $\mathbb{E}^4_1$. We give necessary and sufficient condition for flat spacelike rotational surface to have pointwise 1-type Gauss map. Also, we obtain a characterization for boost invariant marginally trapped surface with pointwise 1-type Gauss map.
KILLING MAGNETIC FLUX SURFACES IN EUCLIDEAN 3-SPACE
Ozdemir, Zehra,Gok, Ismail,Yayli, Yusuf,Ekmekci, F. Nejat The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.2
In this paper, we give a geometric approach to Killing magnetic flux surfaces in Euclidean 3-space and solve the differential equations which expressed the mentioned surfaces. Furthermore we give some examples and draw their pictures by using the programme Mathematica.
BOOST INVARIANT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN MINKOWSKI 4-SPACE E4 1
Ferdag Kahraman Aksoyak,Yusuf Yayli 대한수학회 2014 대한수학회보 Vol.51 No.6
In this paper, we study spacelike rotational surfaces which are called boost invariant surfaces in Minkowski 4-space E41 . We give necessary and sufficient condition for flat spacelike rotational surface to have pointwise 1-type Gauss map. Also, we obtain a characterization for boost invariant marginally trapped surface with pointwise 1-type Gauss map.
FLAT ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN E4
( Ferdag Kahraman Aksoyak ),( Yusuf Yayli ) 호남수학회 2016 호남수학학술지 Vol.38 No.2
In this paper we study general rotational surfaces in the 4- dimensional Euclidean space E4 and give a characterization of fiat general rotational surface with pointwise 1-type Gauss map. Also, we show that a flat general rotational surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Clifford torus.
Killing Magnetic Flux surfaces in Euclidean 3-space
Zehra Ozdemir,Ismail Gok,Yusuf Yayli,F. Nejat EKMEKCI 호남수학회 2019 호남수학학술지 Vol.41 No.2
In this paper, we give a geometric approach to Killing magnetic flux surfaces in Euclidean 3-space and solve the differential equations which expressed the mentioned surfaces. Furthermore we give some examples and draw their pictures by using the programme Mathematica.
FLAT ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN E<sup>4</sup>
Aksoyak, Ferdag Kahraman,Yayli, Yusuf The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.2
In this paper we study general rotational surfaces in the 4-dimensional Euclidean space $\mathbb{E}^4$ and give a characterization of flat general rotational surface with pointwise 1-type Gauss map. Also, we show that a flat general rotational surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Clifford torus.
HARMONIC CURVATURE FUNCTIONS OF SOME SPECIAL CURVES IN GALILEAN 3-SPACE
Yilmaz, Beyhan,Metin, Seyma,Gok, Ismail,Yayli, Yusuf The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.2
The aim of the paper is to characterize some curves with the help of their harmonic curvature functions. First of all, we have defined harmonic curvature function of an arbitrary curve and have re-determined the position vectors of helices in terms of their harmonic curvature functions in Galilean 3-space. Then, we have investigated the relation between rectifying curves and Salkowski (or anti-Salkowski) curves in Galilean 3-space. Furthermore, the position vectors of them are obtained via the serial approach of the curves. Finally, we have given some illustrated examples of helices and rectifying curves with some assumptions.