Homothetic Motions at E4 with Bicomplex Numbers

In this paper, a matrix which is similar to Hamilton operators has been presented to bicomplex numbers in four dimensional Euclidean space E4. We show that if the matrix is obtained from a curve on the Lie group M, then the motion is a homothetic motion. It has been found that the motion defined by a regular curve of order r and derivations curves on the hypersurface M has only one acceleration center of order (r - 1) at every t-instant.