Angle between two complex lines

Abstract

The chordal distance function on a complex projective space algebraically definesan angle between any two complex lines, which is known as the Hermitian angle. In thisexpository paper, we show that one can canonically construct a real line corresponding to eachof these complex lines so that the real angle between these two real lines exactly agrees withthe Hermitian angle between the complex lines. This way, the Hermitian angle is interpretedas a real angle, and some well known results pertaining Hermitian angles are proved usingreal geometry. As an example, we give a direct and elementary proof that the chordal distancefunction satisfies the triangle inequality