ON THE CURVATURE THEORY OF NON-NULL CYLINDRICAL SURFACES IN MINKOWSKI 3-SPACE

ON THE CURVATURE THEORY OF NON-NULL CYLINDRICAL
SURFACES IN MINKOWSKI 3-SPACE

BURAK SAHINER, MUSTAFA KAZAZ, HASAN HUSEYIN UGURLU

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Abstract

This paper presents the curvature theory of non-null cylindrical surfaces
in Minkowski 3-space. The denition of the line of striction and generator trihedron
for cylindrical surfaces in Minkowski 3-space are given. The derivation formulae and
Darboux instantaneous rotation vectors of generator trihedrons which play important
role in robot kinematics are found. Moreover, curvature theory of a Lorentzian circular
cylinder is given as an example.

Keywords

Curvature theory, Cylindrical surface, Darboux instantaneous rotation vector,
Generator trihedron, Minkowski space.