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Mean Value Operators, Differential Operators and D'Atri Spaces |
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| Authors: | Paul Günther† Friedberg Prüfer |
| Affiliation: | (1) Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany |
| Abstract: | We study commutativity relations between differential operators and spherical means on Riemannian manifolds. The results show that all D'Atri spaces are ball-homogeneous. A further consequence characterizes complete nonpositively curved, simply connected D'Atri spaces by commuting mean value operators. |
| Keywords: | commuting differential operators Hadamard manifolds Laplacians spaces with volume-preserving geodesic spherical means |
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