On Parallelizable Spheres in Semi Euclidean Space

In Euclidean space, there exist four theorems which show that S-n sphere is not parallelizable for n not equal 1, 3, 7. While three of them are shown by using Bott theorem, the last one is shown by using Hurwitz-Radon numbers. In this paper, a theorem and the proof of this theorem about parallelization of spheres in semi-Euclidean space is given. It is presented that some spheres are parallelizable with respect to specific number systems.