Can I file any legal action if my manager grabbed my wrists?

You could complain to the police but they have real cases to deal with. Let it go and see if he hangs himself. You can even taunt him now and he can't do anything unless he wants to be fired. So you have him right where he should be. Even a false complaint from you would get him fired.

Lawyers are not inclined to take on a case when there are no physical injuries to base damages on.

Did he cause injury? If not, other than the embarrassment of it, it does not appear to me that there is much there.

Any uninvited touching can result in civil and criminal liability for assault. In a civil case you sue for money damages and in criminal cases you ask the court to take away someone's freedom. As a practical matter, you might want to seriously consider whether you want to go down either or both of these routes, though. The value of any civil case is not likely to be much unless there was a serious permanent injury. Criminal cases have a higher standard of proof and require that you prove he had a criminal intent. Because of that, I would suspect your chances of winning may not be as great. You may want to consult with a criminal lawyer or district attorney as to their advice on that, though. The bottom line is that you will have to continue working under this person, unless you can request a transfer, and so you may want to leave the situation as it is. You have reported it and his superiors are aware of the problem. If it happens again, you will be able to show the Employer was on notice, which could possibly open it up to a claim for punishment damages.

You could sue him for assault, but it would probably be hard to collect. You could ask the employer to move him or you, but there is little you can do if they will not. If there are more instances in the future, you could sue your employer if they do not do more to prevent it. However, you probably do not have a viable suit against the employer for just one incident.

You can file a civil complaint for battery. Depending on the facts, false imprisonment and intentional infliction of emotional distress may apply.

Theoretically, yes, but as a practical matter it is not worth pursuing.

Did you complaint to HR about it? You might be able to bring a legal claim against the manager but without any permanent injury you case might not be worth very much.