Abstract
SynopsisLet Mm (r, f) denote the mean-value of a real-valued integrable function f over a geodesic sphere with centre m and radius r in an n-dimensional Riemannian manifold M. We obtain an expansion of Mm (r, f) in powers of r, thereby generalizing Pizzetti's formula valid in euclidean space. From this expansion we prove that the propertyfor every harmonic function near m, characterizes Einstein spaces. We define super-Einstein spaces and prove that they are characterized by the property
Publisher
Cambridge University Press (CUP)
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