The principal circle bundle S²ⁿ⁺¹(Pⁿ(C), S¹)

Abstract

It is well known that an odd-dimensional sphere is a circle bundle over the complex projective space (see [33]). Consequently, many geometric properties of the complex projective space are inherited from those of the sphere. Especially, at the end of this section, we prove that the complex projective space has constant holomorphic sectional curvature.