JournalszaaVol. 4, No. 3pp. 235–249

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

  • Rainer Schimming

    Ernst-Moritz-Arndt-Universität Greifswald, Germany
Riemannian Manifolds for which a Power of the Radius is $k$-harmonic cover

Abstract

Let σ=σ(x,y)\sigma = \sigma (x, y) denote Synge’s function of a Riemannian manifold (M,g)(M, g) of any signature and consider the condition that some power of σ\sigma or the logarithm of σ\sigma is kk-harmonic. Then in many, cases (M,g)(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 kk-harmonic. Z. Anal. Anwend. 4 (1985), no. 3, pp. 235–249

DOI 10.4171/ZAA/149