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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 dimM=n2. 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.


MSC:
53C20Global Riemannian geometry, including pinching
57S05Topological properties of groups of homeomorphisms or diffeomorphisms
53A30Conformal differential geometry
References:
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