281 research outputs found
Timelike Bertrand Curves in Semi-Euclidean Space
In this paper, it is proved that, no special timelike Frenet curve is a
Bertrand curve in and also, in , such that the notion of Bertrand curve is definite only in
and . Therefore, a generalization of timelike
Bertrand curve is defined and called as timelike (1,3)-Bertrand curve in
. Moreover, the characterization of timelike (1,3)-Bertrand
curve is given in
Lamarle Formula in 3-Dimensional Lorentz Space
The Lamarle Formula, given by Kruppa in \cite{Kr}, is known as a relationship
between the Gaussian curvature and the distribution parameter of a ruled
surface in the surface theory. The ruled surfaces were investigated in 3
different classes with respect to the character of base curves and rulings,
\cite{Tu1},\cite{Tu2}. In this paper on account of these studies, the
relationships between the Gaussian curvatures and distribution parameters of
spacelike ruled surface, timelike ruled surface with spacelike ruling and
timelike ruled surface with timelike ruling are obtained, respectively. These
relationships are called as Lorentzian Lamarle formulas. Finally some examples
concerning with these relations are given
Commutative Quaternion Matrices
In this study, we introduce the concept of commutative quaternions and
commutative quaternion matrices. Firstly, we give some properties of
commutative quaternions and their Hamilton matrices. After that we investigate
commutative quaternion matrices using properties of complex matrices. Then we
define the complex adjoint matrix of commutative quaternion matrices and give
some of their properties
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