On the Darboux vector of ruled surfaces in pseudo-Galilean space
In the Euclidean space the Darboux vector may be interpreted kinematically as the direction
of the instantaneous axis of rotation in the moving trihedron. In this paper we mainly study
the Darboux vector of ruled surfaces in pseudo-Galilean space. We obtain relationships
between Darboux and Frenet vectors of each type of ruled surfaces in pseudo-Galilean
space. Moreover we observe that in the pseudo-Galilean space the Darboux vector can be
interpreted kinematically as a shear along the absolute line.
of the instantaneous axis of rotation in the moving trihedron. In this paper we mainly study
the Darboux vector of ruled surfaces in pseudo-Galilean space. We obtain relationships
between Darboux and Frenet vectors of each type of ruled surfaces in pseudo-Galilean
space. Moreover we observe that in the pseudo-Galilean space the Darboux vector can be
interpreted kinematically as a shear along the absolute line.
Abstract
In the Euclidean space the Darboux vector may be interpreted kinematically as the direction of the instantaneous axis of rotation in the moving trihedron. In this paper we mainly study the Darboux vector of ruled surfaces in pseudo-Galilean space. We obtain relationships between Darboux and Frenet vectors of each type of ruled surfaces in pseudo-Galilean space. Moreover we observe that in the pseudo-Galilean space the Darboux vector can be interpreted kinematically as a shear along the absolute line.
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