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Considering complex projective $k$-space as the homogeneous space $SU_k/U_{k-1}$, is it true that every $SU_k$-invariant form is closed?

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    $\begingroup$ Citing from the master: mathoverflow.net/a/158565/21123 $\endgroup$
    – alvarezpaiva
    Commented Dec 2, 2014 at 13:05
  • $\begingroup$ So yes, complex projective space is a symmetric space and its invariant forms are harmonic and, therefore, closed. $\endgroup$
    – alvarezpaiva
    Commented Dec 2, 2014 at 13:06

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