## 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

### MSC:

 53B20 Local Riemannian geometry

### Citations:

Zbl 0571.53012; Zbl 0628.53057