Abstract
A complete treatment of one parameter homothetic motions in three and four dimensional Euclidean spaces is provided in the Yayli's PhD thesis (Yayli, 1988). Here we follow his idea to define one parameter homothetic motion in generalized 3-space By means of the generalized Hamilton operators, we also define a Hamilton motion and show that it is a homothetic motion. We investigate some properties of this motion and show that Darboux vector of the motion can be written as multiplication of two generalized quaternions.
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