Abstract: In this work, position vector of a time-like dual curve
according to standard frame of D31
is investigated. First, it is proven
that position vector of a time-like dual curve satisfies a dual vector
differential equation of fourth order. The general solution of this dual
vector differential equation has not yet been found. Due to this, in
terms of special solutions, position vectors of some special time-like
dual curves with respect to standard frame of D31
are presented.
Abstract: In this paper, we carry over some of the results which
are valid on a certain class of Moufang-Klingenberg planes M(A)
coordinatized by an local alternative ring A := A(ε) = A+Aε of
dual numbers to finite projective Klingenberg plane M(A) obtained
by taking local ring Zq (where prime power q = pk) instead of A.
So, we show that the collineation group of M(A) acts transitively
on 4-gons, and that any 6-figure corresponds to only one inversible
m ∈ A.
Abstract: In this paper we are interested in Moufang-Klingenberg
planesM(A) defined over a local alternative ring A of dual numbers.
We show that some collineations of M(A) preserve cross-ratio.
Abstract: In this paper we are interested in Moufang-Klingenberg
planesM(A) defined over a local alternative ring A of dual numbers.
We introduce two new collineations of M(A).
Abstract: In this paper we are interested in Moufang-Klingenberg
planesM(A) defined over a local alternative ring A of dual numbers.
We show that a collineation of M(A) preserve cross-ratio. Also, we
obtain some results about harmonic points.