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Zeitschrift für Analysis und ihre Anwendungen


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Volume 4, Issue 3, 1985, pp. 235–249
DOI: 10.4171/ZAA/149

Published online: 1985-06-30

Riemannian Manifolds for which a Power of the Radius is $k$-harmonic

Rainer Schimming[1]

(1) Ernst-Moritz-Arndt-Universität Greifswald, Germany

Let $\sigma = \sigma (x, y)$ denote Synge’s function of a Riemannian manifold $(M, g)$ of any signature and consider the condition that some power of $\sigma$ or the logarithm of $\sigma$ is $k$-harmonic. Then in many, cases $(M, g)$ turns out to be flat. Certain classes of non-flat manifolds can be characterized just by a condition of the aforesaid typo.

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Schimming Rainer: Riemannian Manifolds for which a Power of the Radius is $k$-harmonic. Z. Anal. Anwend. 4 (1985), 235-249. doi: 10.4171/ZAA/149