On the blaschke invariants of the pair of the generalized ruled surfaces under the symmetric homothetic motion in En

ON THE BLASCHKE INVARIANTS OF THE PAIR OF THE GENERALIZED RULED SURFACES UNDER THE SYMMETRIC HOMOTHETIC MOTION IN En SUMMARY Keywords: Euclidean Space, Ruled Surface, Symmetric Homothetic Motion, Blaschke Invariant. This work is prepared as four chapters. In the first chapter one-parameter motion and one-parameter homothetic motion are defined in E" and their definitions and theorems are given. In the second chapter of this work we have given the ruled surfaces in three dimensional Euclidean space, E3. After that (&+l)-dimensional ruled surfaces in n - dimensional Euclidean space are explained and the definitions and the theorems related to the asymptotic and tangential bundles of these ruled surfaces are given. Furthermore, definitions related to the z.th principal distribution parameter of (k + l)- dimensional ruled surface, total distribution parameter and Blaschke invariants are also given. In the third chapter of the thesis the pair of (k+l)- dimensional ruled surfaces under homothetic motion in E" are investigated and related phenomena are expressed. Fourth chapter of this work is the original contribution to the science of mathematics. In this chapter we have given the theorems and the results of the Blaschke invariants of (&+l)-dimensional ruled surface pairs under symmetric homothetic motion in n - dimensional Euclidean space, E". Vll