Article PDF
References
Berger, M., Gauduchon, P. and Mazet, E.:Le spectre d'une variété riemannienne, Lecture Notes in Mathematics, 194, Springer-Verlag, Berlin, 1971.
Besse, A.L.:Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik, 93, Springer-Verlag, Berlin, 1978.
Chen, B.Y. and Vanhecke, L.: Differential geometry of geodesic spheres,J. Reine Angew. Math. 325 (1981), 28–67.
D'atri, J.E. and Nickerson, H.K.: Geodesic symmetries in spaces with special curvature tensor,J. Differential Geometry 9 (1974), 251–262.
D'atri, J.E.: Geodesic spheres and symmetries in naturally reductive homogeneous spaces,Michigan Math. J. 22 (1975), 71–76.
Gray, A. and Vanhecke, L.: Riemannian geometry as determined by the volumes of small geodesic balls,Acta M Math. 142 (1979), 157–198.
Kowalski, O. and Vanhecke, L.: Opérateurs différentiels invariants et symmétries géodesiques préservant le volume,C.R. Acad. Sc. Paris, Série I 296 (1983), 1001–1003.
Kowalski, O. and Vanhecke, L. : A generalization of a theorem on naturally reductive homogeneous spaces,Proc. Amer. Math. Soc., to appear.
Lichnerowicz, A.: Opérateurs différentiels invariant sur un espace homogéne,Ann. Sc. Ecole Norm. Sup. 81 (1964), 341–385.
Roberts, P.H. and Ursell, H.D.: Random walk on a sphere and on a Riemannian manifold,Phil. Trans. Royal Soc. London A 252 (1960), 317–356.
Ruse, H.S.: On commutative Riemannian manifolds,Tensor 26 (1972), 180–184.
Ruse, H.S., Walker, A.G. and Willmore, T.J. :Harmonic spaces, Cremonese, Roma, 1961.
Sumitomo, T.: On a certain class of Riemannian homogeneous spaces,Colloq. Math. 26 (1971), 129–133.
Sumitomo, T.: On the commutator of differential operators,Hokkaido Math. J. 1 (1972), 30–42.
Vanhecke, L.: 1-harmonic spaces are harmonic,Bull. London Math. Soc. 13 (1981), 409–411.
Vanhecke, L.: A note on harmonic spaces,Bull. London Math. Soc. 13 (1981), 545–546.
Vanhecke, L.: A conjecture of Besse on harmonic manifolds,Math. Z. 178 (1981), 555–557.
Vanhecke, L.: Some solved and unsolved problems about harmonic and commutative spaces,Bull. Soc. Math. Belg. B34 (1982), 1–24.
Vanhecke, L. and Willmore, T.J.: Riemannian extensions of D'Atri spaces,Tensor 38 (1982), 154–158.
Vanhecke, L.: The canonical geodesic involution and harmonic spaces,Ann. Global Analysis and Geometry 1 (1983), 131–136.
Vanhecke, L. and Willmore, T.J.: Interaction of tubes and spheres,Math. Ann. 263 (1983), 31–42.
Willmore, T.J.: 2-point invariant functions and k-harmonic manifolds,Rev. Rouwaine Math. Pures Appl. 13 (1968), 1051–1057.
Willmore, T.J. and El Hadi, K.: k-harmonic symmetric manifolds,Rev. Roumaine Math. Pures Appl. 15 (1970), 1573–1577.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor T.J. Willmore
Rights and permissions
About this article
Cite this article
Kowalski, O., Vanhecke, L. Two-point functions on Riemannian manifolds. Ann Glob Anal Geom 3, 95–119 (1985). https://doi.org/10.1007/BF00054493
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00054493