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References
A.L. Besse, Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik, 93, Springer-Verlag, Berlin, 1978.
P. Carpenter, A. Gray and T.J. Willmore, The curvature of Einstein symmetric spaces, Quart. J. Math. Oxford 33 (1982), 45–64.
B.Y. Chen and L. Vanhecke, Differential geometry of geodesic spheres, J. Reine Angew. Math. 325 (1981), 28–67.
J.E. D'Atri and H.K. Nickerson, Divergence-preserving geodesic symmetries, J. Differential Geometry 3 (1969), 467–476.
J.E. D'Atri and H.K. Nickerson, Geodesic symmetries in spaces with special curvature tensor, J. Differential Geometry 9 (1974), 251–262.
J.E. D'Atri, Geodesic spheres and symmetries in naturally reductive homogeneous spaces, Michigan Math. J. 22 (1975), 71–76.
A. Derdziński, Self-dual Kähler manifolds and Einstein manifolds of dimension four, Compositio Math. 49 (1983), 405–433.
D. Ferus, H. Karcher and H.F. Münzner, Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z. 177 (1981), 479–502.
A. Gray, The volume of a small geodesic ball in a Riemannian manifold, Michigan Math. J. 20 (1973), 329–344.
A. Gray and L. Vanhecke, Riemannian geometry as determined by the volumes of small geodesic balls, Acta Math. 142 (1979), 157–198.
G.R. Jensen, Homogeneous Einstein spaces of dimension four, J. Differential Geometry 3 (1969), 309–349.
O. Kowalski and L. Vanhecke, Ball-homogeneous and disk-homogeneous Riemannian manifods, Math. Z. 180 (1982), 429–444.
O. Kowalski, Spaces with volume-preserving symmetries and related classes of Riemannian manifolds, Rend. Sem. Mat. Univ. e Politec. Torino, to appear.
K. Sekigawa, On 4-dimensional connected Einstein spaces satisfying the condition R(X,Y)·R = 0, Sem. Rep. Niigata Univ. A7 (1969), 29–31.
K. Sekigawa, On the Riemannian manifolds of the form B×fF, Kōdai Math. Sem. Rep. 26 (1975), 343–347.
K. Sekigawa, On some 3-dimensional curvature homogeneous spaces, Tensor 31 (1977), 87–97.
K. Sekigawa and L. Vanhecke, Symplectic geodesic symmetries on Kähler manifolds, Quart. J. Math. Oxford, to appear.
I.M. Singer, Infinitesimally homogeneous spaces, Comm. Pure. Appl. Math. 13 (1960), 685–697.
I.M. Singer and J.A. Thorpe, The curvature of 4-dimensional Einstein spaces, in Global Analysis (Papers in honor of K. Kodaira), Princeton University Press, Princeton 1969, 355–366.
H. Takagi, On curvature homogeneity of Riemannian manifolds, Tōhoku Math. J. 26 (1974), 581–585.
L. Vanhecke, A note on harmonic spaces, Bull. London Math. Soc. 13 (1981), 545–546.
L. Vanhecke, Some results about homogeneous structures on Riemannian manifolds, Differential Geometry, Proc. Conf. Differential Geometry and its Applications, Nové Město 1983, Univerzita Karlova, Praha, 1984, 147–164.
Y.L. Xin, Remarks on characteristic classes of four-dimensional Einstein manifolds, J. Math. Phys. 21 (1980), 343–346.
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Sekigawa, K., Vanhecke, L. (1986). Volume-preserving geodesic symmetries on four-dimensional Kähler manifolds. In: Naveira, A.M., Ferrández, A., Mascaró, F. (eds) Differential Geometry Peñíscola 1985. Lecture Notes in Mathematics, vol 1209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076638
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DOI: https://doi.org/10.1007/BFb0076638
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