Journal of Differential Geometry

A Characterization of harmonic spaces

Balázs Csikós and Márton Horváth

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The authors proved in "On the volume of the intersection of two geodesic balls," Differential Geom. Appl. 29 (2011), 567–576, that in a complete, connected, and simply connected Riemannian manifold, the volume of the intersection of two small geodesic balls depends only on the distance between the centers and the radii if and only if the space is harmonic. In this paper, we show that this proposition remains true, if the condition is restricted to balls of equal radii.

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J. Differential Geom., Volume 90, Number 3 (2012), 383-389.

First available in Project Euclid: 24 April 2012

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Csikós, Balázs; Horváth, Márton. A Characterization of harmonic spaces. J. Differential Geom. 90 (2012), no. 3, 383--389. doi:10.4310/jdg/1335273388.

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