The Fubini–Study metric on the complex projective plane CP has been proposed as a gravitational instanton, the gravitational analog of an instanton. The metric, the connection form and the curvature are readily computed, once suitable real 4D coordinates are established. Writing ( x , y , z , t ) for real Cartesian coordinates, one then defines polar coordinate one-forms on the 4-sphere (the quaternionic projective line) as