Isotropic vector fields on spheres, spinor structures on spheres and projective spaces (Q1178350)

This is a continuation of [ Kodai Math. J. 7, 203-207 (1984; Zbl 0554.53027)]\ in which a previous result of the author is reproven and strengthened to yield the theorem that a \(C^ \infty\) complexified tangent bundle of any sphere is trivializable. The paper concludes with an elementary discussion of existence conditions for spinor structures on spheres and projective spaces based on the author's work on isotropic vector fields.