Vector Fields on the Sphere

Abstract

In Chap. 12, Theorem (8.2), we saw that S^{n −1} has ρ(n) − 1 orthonormal tangent vector fields defined on it. The object of this chapter is to outline the steps required to prove that S^{n −1} does not have ρ(n) orthonormal tangent vector fields defined on it; in fact, S^{n −1} does not have ρ(n) linearly independent tangent vector fields; see also Adams [6].