Abstract
We prove that any maximal geodesic in a weakly symmetric space is an orbit of a one-parameter group of isometries of that space.
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Berndt, J., Ricci, F. and Vanhecke, L.: Weakly symmetric groups of Heisenberg type, preprint, 1996.
Berndt, J., Tricerri, F. and Vanhecke, L.: Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces, Lecture Notes in Mathematics, Vol. 1598, Springer-Verlag, Berlin, Heidelberg, 1995.
Berndt, J. and Vanhecke, L.: Geometry of weakly symmetric spaces, J. Math. Soc. Japan 48 (1996), 745-760.
Chevalley, C.: Theory of Lie Groups, Princeton University Press, Princeton, 1946.
Greub, W., Halperin, S. and Vanstone, R.: Connections, Curvature, and Cohomology, II, Academic Press, New York, London, 1973.
Kobayashi, S. and Nomizu, K.: Foundations of Differential Geometry, I, II, Interscience Publishers, New York, 1963, 1969.
Kowalski, O. and Vanhecke, L.: Riemannian manifolds with homogeneous geodesics, Boll. Un. Mat. Ital. B (7) 5 (1991), 189-246.
Selberg, A.: Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47-87.
Varadarajan, V. S.: Lie Groups, Lie Algebras, and Their Representations, Graduate Texts in Mathematics, Vol. 102, Springer-Verlag, New York, 1984.
Ziller, W.: Homogeneous Einstein metrics on spheres and projective spaces, Math. Ann. 259 (1982), 351-358.
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Berndt, J., Kowalski, O. & Vanhecke, L. Geodesics in Weakly Symmetric Spaces. Annals of Global Analysis and Geometry 15, 153–156 (1997). https://doi.org/10.1023/A:1006565909527
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DOI: https://doi.org/10.1023/A:1006565909527