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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 $C\left(M\right)$ be the whole conformal group of a Riemannian manifold $M$ with $dimM=n\ge 2$. If $M$ is not conformally equivalent with ${S}^{n}$ or ${E}^{n}$, then $C\left(M\right)$ 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.

##### MSC:
 53C20 Global Riemannian geometry, including pinching 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms 53A30 Conformal differential geometry
##### Keywords:
conformal group; Riemannian manifold
##### References:
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