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I have heard somewhere that a conformal map between Riemannian manifolds is determined by its second jet at a single point. (assuming the source manifold is connected).

Where can I find a reference for this fact?

Asaf Shachar
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    At the very least you should assume that dimension is $>2$. I think, the statement is correct in this case, check the book "Transformation Groups in Differential Geometry" by Kobayashi. – Moishe Kohan Mar 07 '18 at 05:01

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The answer is positive once you assume that your manifold is connected and has dimension $\ge 3$. The proof is the same as the one of Theorem 6.1 in

"Transformation Groups in Differential Geometry" by S.Kobayashi.

(See also Theorem 3.1 of the same book.) The key is that in dimensions $\ge 3$, a conformal structure is uniquely determined by a Cartan connection on the 2-frame bundle over your manifold.

If you are doing conformal geometry, I suggest you spend some time (but not too long) reading Kobayashi's book.

Moishe Kohan
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