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

### Rainer Schimming

Ernst-Moritz-Arndt-Universität Greifswald, Germany

## Abstract

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.

## Cite this article

Rainer Schimming, Riemannian Manifolds for which a Power of the Radius is $k$-harmonic. Z. Anal. Anwend. 4 (1985), no. 3, pp. 235–249

DOI 10.4171/ZAA/149