  We study a class of generalized self-duality relations in gauge theories on
the complex projective space with the Fubini-Study metric. Our theories consist
of only gauge fields with gauge group U(n). The pseudo-energies which we
consider contain higher orders of field strength and are labeled by an integer
p smaller than or equal to [n/2]. For making the Bogomol'nyi completion we need
non-single trace terms in the pseudo-energies, unlike the models defined on
spheres, which were studied previously. We construct an explicit solution of
codimension 2n to generalized self-duality equations as Bogomol'nyi equations,
by using a part of the spin connection.
