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.KeywordsTangent VectorAhler ManifoldComplex Projective SpaceComplex Space FormHorizontal LiftThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.