Here are three objective statements for a project manager position:
"A career oriented and ambitious project manager seeking a challenging project management position in a growth oriented company"
The above one may be perceived as a bit arrogant (I also think it's a bit repetitive), especially when read by a manager that has lots of insecurities, the below one is probably better.
"A project manager with X years of experience looking for a long term career in a project oriented [add industry here, for example "construction"] company."
Now here's the last one that I think is the best of the bunch:
"A project manager with a proven track record of successful project delivery is seeking a long term career in a [add industry here] company".
I think the term "long term career" is important, especially when you're looking for a career. Employers like candidates that are willing to commit for a long time...
It is important to change your objective statement (and parts of your CV) depending on the company you're sending the CV to. Sending the same CV to every single company you see looking for a job, with no modifications, will rarely, if ever, land you a job. The key is to adjust your experience and highlight the relevant knowledge that you have to the company's business/industry.