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@Amr: Presumably, what you want is the application of Weyl's theorem about scalar invariants of representations of the orthogonal group applied to the normalized power series expansion of metrics in normal coordinates. See H. Weyl's "The Classical Groups" (the chapter on the orthogonal group) and P. Gilkey's discussion in Section 2.4 of his book "Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem".
@QGravity: The best reference I know is Helgason's "Differential Geometry, Lie groups, and Symmetric Spaces". See Table V of Chapter X, Section 6. If all you want is the classification of the compact real forms of the simple Lie groups, that's much easier and follows directly from the classification of the complex simple Lie algebras over $\mathbb{C}$, but, if you want all the real forms, you need to know the finite order automorphisms of the complex simple Lie algebras, which is more delicate.
Added a little more information to show that the example constructed really is a smooth metric on the 2-sphere, plus a remark showing that there are lots of examples with no symmetry at all.
Look in Helgason's Differential Geometry, Lie Groups, and Symmetric Spaces. He gives a formula for the Jacobian of the differential of the exponential map. I don't know the history that well, but I think that such formulae are due originally to some combination of Cartan and Weyl. Probably, Helgason's notes at the end of the relevant chapter contain some comment on this. (I don't have my copy handy at the moment.)
