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.

MathOverflow Questions:

Conformal covers of all degrees


53C20 Global Riemannian geometry, including pinching
57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
53A30 Conformal differential geometry (MSC2010)
Full Text: DOI EuDML


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