Differential Geometry
The natural metric on CPn is the Fubini-Study metric, and its isometry group is the projective unitary group PU(n+1), where the stabilizer of a point is
It is a Hermitian symmetric space (Kobayashi & Nomizu 1996), represented as a coset space
The geodesic symmetry at a point p is the unitary transformation that fixes p and is the negative identity on the orthogonal complement of the line represented by p.
Read more about this topic: Complex Projective Space
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