The k-harmonic spaces. (English) Zbl 0674.53027

Pr. Nauk. Politech. Szczec. 323, Inst. Mat. 9, 67-71 (1987).
Let (M,g) be a pseudo-Riemannian manifold and denote by \(\sigma\) Synge’s two-point function. (For a proper Riemannian manifold \(2\sigma\) equals the square of the geodesic distance between two points which are not too far from each other.) Further, let \(\Delta\) denote the Laplacian of (M,g). Several authors have treated manifolds such that \(\Delta^ k| \sigma |^{\ell}=0\) for a positive integer k and a real number \(\ell\). See [R. Schimming, Z. Anal. Anwend. 4, 235-249 (1985; Zbl 0571.53012)] and [R. Schimming and J. Kowolik, ibid. 6, 331- 339 (1987; Zbl 0628.53057)] for further details and references.
In this short note, which is not an example of a clearly and correctly written paper, the authors treat the case where M is Euclidean n-space and prove a theorem which is already included in the papers mentioned above.
[Editorial note: The third author has informed us, that he gave no authorization to publish this article under his name and that he is not responsible for its contents.]
Reviewer: L.Vanhecke


53B20 Local Riemannian geometry