A New Approach To Homothetic Motions and surfaces with Tessarines

Abstract

This paper is a detailed study on homothetic motions, surfaces and Lie groups by considering the product and addition rules and conjugates of the tessarines which is given according to the arbitrary unit i#8321. To do these, we define a matrix that is similar to Hamilton operators and give some algebraic properties of this matrix. And then, we introduce different the surfaces and different hyperquadrics . Also by using the homothetic motions we give some special subgroups of Lie groups and reparametrize the surfaces nbs