# isometry group of the riemannian manifold $\mathbb{T}^2$?

What is the isometry group of the riemannian manifold $\mathbb{T}\times \mathbb{T}$ where $\mathbb{T}=\{z\in \mathbb{C}\ :\ |z|=1\}$ is the classical torus?

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Is this a homework problem? What have you tried so far? Do you have thoughts on what the answer should be? – Aaron Jan 25 '12 at 17:53
I know the isometry group of $\mathbb{T}$. More generally, how to compute the isometry group of a product manifold? I does not think that it is the product of isometry groups in the general case. – Zouba Jan 25 '12 at 17:58