Harmonic radial vector fields on harmonic spaces

[摘要] We characterize harmonic spaces in terms of the dimensions of various spaces of radial eigen-spaces of the Laplacian Delta(0) on functions and the Laplacian Delta(1) on 1-forms. We examine the nature of the singularity as the geodesic distance r tends to zero of radial eigen-functions and 1-forms. Via duality, our results give rise to corresponding results for radial vector fields. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Harmonic spaces;Density function;Harmonic vector fields;Radial eigen-spaces of the Laplacian