On Some Real Hypersurfaces of a Complex Projective Space

A principal circle bundle over a real hypersurface of a complex projective space CPⁿ can be regarded as a hypersurface of an odd-dimensional sphere. From this standpoint we can establish a method to translate conditions imposed on a hypersurface of CPⁿ into those imposed on a hypersurface of S^{2n + 1}. Some fundamental relations between the second fundamental tensor of a hypersurface of CPⁿ and that of a hypersurface of S^{2n + 1} are given.