Rigidity is established for isotropic harmonic maps from the 2-torus to CP space arising from complete linear systems, and for broader holomorphic embeddings lacking hyperosculation points when Fubini-Study pullbacks satisfy an extra condition.
Griffiths,On Cartan’s method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry,Duke Mathematical Journal41(1974) 775
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Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective space
Rigidity is established for isotropic harmonic maps from the 2-torus to CP space arising from complete linear systems, and for broader holomorphic embeddings lacking hyperosculation points when Fubini-Study pullbacks satisfy an extra condition.