Nonexistence conjecture for compact Clifford–Klein forms of SO(2,2m+1)/SU(1,m)

For $m\geq 1$, consider the homogeneous space

$$\operatorname{SO}(2,2m+1)/\operatorname{SU}(1,m).$$

A compact Clifford–Klein form is a compact quotient of this space by a discrete group acting properly.

Nonexistence conjecture for $\operatorname{SO}(2,2m+1)/\operatorname{SU}(1,m)$. The homogeneous space

$$\operatorname{SO}(2,2m+1)/\operatorname{SU}(1,m)$$

does not have a compact Clifford–Klein form.

The paper presents this as a special case of the general reductive-subgroup conjecture because no suitable reductive subgroup exists in this case. The supplied text gives no evidence that this special case has been resolved.