On projective Anosov subgroups of symplectic groups

We prove that a word hyperbolic group whose Gromov boundary properly contains a 2-sphere cannot admit a projective Anosov representation into Sp₂₌ (C), m N. We also prove that a word hyperbolic group which admits a projective Anosov representation into Sp₂₌ (R) is virtually a free group or virtually a surface group, a result established indepedently by Dey-Greenberg-Riestenberg.