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Hi, Dear colleague, is there any survey paper on the classification theorems on Lagrangian submanifolds in a Complex space form with parallel mean curvature vector? and any insight from you on this subject is welcome.

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up vote 4 down vote accepted

I was recently reading this nice survey by Amarzaya-Ohnita, and they have an entire section on the subject you are interested (see Section 3). They claim that totally real submanifolds with parallel mean curvature vector in $\mathbb C^n$ and $\mathbb C P^n$ have been classified by Naitoh and Takeuchi (references 8, 9, 10 & 11 in their bibliography). Maybe you should take a look at those papers too.

As a side note, just googling "Lagrangian submanifold parallel mean curvature vector" you get lots of interesting links...

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Thanks Renato. Your reference is very usefully and I have great interest with it. – Mathboy Dec 6 '12 at 23:09

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