#### DOCUMENTA MATHEMATICA, Vol. 19 (2014), 1017-1023

L. Biliotti, A. Ghigi, and P. Heinzner

A Remark on the Gradient Map

For a Hamiltonian action of a compact group \$U\$ of isometries on a compact Kähler manifold \$Z\$ and a compatible subgroup \$G\$ of \$U^\C\$, we prove that for any closed \$G\$--invariant subset \$Y\subset Z\$ the image of the gradient map \$\mup(Y)\$ is independent of the choice of the invariant Kähler form \$\om\$ in its cohomology class \$[\om]\$.

2010 Mathematics Subject Classification: 53D20

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