Journal of Differential Geometry

A Characterization of harmonic spaces

Balázs Csikós and Márton Horváth

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 24 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1335273388

Digital Object Identifier
doi:10.4310/jdg/1335273388

Mathematical Reviews number (MathSciNet)
MR2916040

Zentralblatt MATH identifier
1244.53043

Citation

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


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