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The action of conformal transformations on a Riemannian manifold. (English) Zbl 0866.53027
“The following assertion was accepted for twenty years when, in 1992, R. J. Zimmer and K. R. Gutschera discovered a very important gap in the only known proof of it: Theorem A. Let $C(M)$ be the whole conformal group of a Riemannian manifold $M$ with $\dim M=n\geq 2$. If $M$ is not conformally equivalent with $S^n$ or $E^n$, then $C(M)$ is inessential, i.e., can be reduced to a group of isometries by a conformal change of metric.” The author’s purpose is to give a new, independent proof of the theorem.

53C20Global Riemannian geometry, including pinching
57S05Topological properties of groups of homeomorphisms or diffeomorphisms
53A30Conformal differential geometry
Full Text: DOI EuDML
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