There's no definitive answer to this question, as burglars may be deterred by different things in different situations. However, it's reasonable to assume that curtains could potentially deter a burglar looking for an easy target, since they would block the view into the home and make it more difficult to assess whether or not it would be worth breaking in. In addition, if the burglar was able to see inside and saw that the home was well-protected with security measures such as alarm systems and cameras, they might be less likely to attempt a break-in. Ultimately, though, it's impossible to say for sure whether or not curtains would deter a burglar in any given situation.