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In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids the nice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial

An intrinsic approach to Lichnerowicz conjecture