Rotations and Screw Motion with Timelike Vector in 3-Dimensional Lorentzian Space

2011 ◽  
Vol 22 (4) ◽  
pp. 1081-1091 ◽  
Author(s):  
Osman Keçilioğlu ◽  
Siddika Özkaldi ◽  
Halit Gündoğan
Keyword(s):  
Timelike Vector ◽  
Lorentzian Space ◽  
3 Dimensional ◽  
Screw Motion

On the explicit characterization of spherical curves in 3-dimensional Lorentzian space L3

2003 ◽  
Vol 11 (4) ◽  
pp. 389-397
Author(s):  
K. Ilarslan ◽  
C. Camci ◽  
H. Kocayigit ◽  
H. H. Hacisalihoglu
Keyword(s):  
Lorentzian Space ◽  
3 Dimensional ◽  
Explicit Characterization

On the explicit characterization of spherical curves in 3-dimensional Lorentzian space

2003 ◽  
Vol 11 (4) ◽  
pp. 389-397
Author(s):  
K. Ilarslan ◽  
C. Camci ◽  
H. Kocayigit ◽  
H. H. Hacisalihoglu
Keyword(s):  
Lorentzian Space ◽  
3 Dimensional ◽  
Explicit Characterization

On Harmonic Curvatures of Null Curves of the AW(k)-Type in Lorentzian Space

2008 ◽  
Vol 63 (5-6) ◽  
pp. 248-252 ◽  
Author(s):  
Mihriban Külahcı ◽  
Mehmet Bektaş ◽  
Mahmut Ergüt
Keyword(s):  
Lorentzian Space ◽  
3 Dimensional ◽  
Null Curves

We investigate null curves of the AW(k)-type (1 ≤ k ≤ 3) in the 3-dimensional Lorentzian space, L3, and give curvature conditions of these curves by using the Cartan frame. Moreover, we study harmonic curvatures of curves of AW(k)-type and show that if the α Frenet curve is of type AW(1), then α is a null helix.

A METHOD TO CONSTRUCT 4-DIMENSIONAL SPACETIMES WITH A SPACELIKE CIRCLE ACTION

2009 ◽  
Vol 06 (04) ◽  
pp. 667-681
Author(s):  
STEFAN HAESEN ◽  
FRANCISCO J. PALOMO ◽  
ALFONSO ROMERO
Keyword(s):  
Vector Fields ◽  
General Procedure ◽  
Lorentzian Manifold ◽  
Convergence Condition ◽  
Circle Action ◽  
Timelike Vector ◽  
3 Dimensional ◽  
Dimensional Spacetime ◽  
Null Congruence

A general procedure to construct a 4-dimensional spacetime from a 3-dimensional time-oriented Lorentzian manifold and each of its timelike vector fields is exposed. It is based on the construction of the null congruence Lorentzian manifold. As an application, examples of stably causal spacetimes which obey the timelike convergence condition, are semi-symmetric, and admit an isometric spacelike circle action are obtained.

Spherical kinematics in 3-dimensional generalized space

2020 ◽  
pp. 2150033
Author(s):  
Erhan Ata ◽  
Ümi̇t Zi̇ya Savci
Keyword(s):  
Matrix Equation ◽  
Orthogonal Matrix ◽  
Matrix Form ◽  
Euler Parameters ◽  
Lorentzian Space ◽  
Split Quaternions ◽  
3 Dimensional ◽  
Unit Quaternions ◽  
Special Cases ◽  
Generalized Quaternion

In this study, we obtained generalized Cayley formula, Rodrigues equation and Euler parameters of an orthogonal matrix in 3-dimensional generalized space [Formula: see text]. It is shown that unit generalized quaternion, which is defined by the generalized Euler parameters, corresponds to a rotation in [Formula: see text] space.We found that the rotation in matrix equation forms using matrix form of the generalized quaternion product. Besides, in [Formula: see text] space, we obtained the rotations determined by the unit quaternions and unit split quaternions, which are special cases of generalized quaternions for [Formula: see text] in 3-dimensional Eulidean space [Formula: see text] in 3-dimensional Lorentzian space [Formula: see text] respectively.

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