Antipodal manifolds in compact symmetric spaces of rank one
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- by Juan Alfredo Tirao PDF
- Proc. Amer. Math. Soc. 72 (1978), 143-149 Request permission
Abstract:
Let M be a compact Riemannian globally symmetric space of rank one. A theorem due to Helgason states that the antipodal manifold ${A_x}$ of a point $x \in M$ is again a symmetric space of rank one. We compute the multiplicities of the restricted roots of ${A_x}$ from those of M, obtaining a very convenient way to determine ${A_x}$.References
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É. Cartan, Sur certaines formes riemannienes remarquables des géométries a groupe fondamental simple, Ann. Sci. École Norm. Sup. 44 (1927), 345-467.
R. Gandulfo and J. Tirao, Multiplier transformations of functions on compact two-point homogeneous spaces, Trabalhos de Matemática 126 (1977).
- Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
- Sigurđur Helgason, The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math. 113 (1965), 153–180. MR 172311, DOI 10.1007/BF02391776
- Tadashi Nagano, Homogeneous sphere bundles and the isotropic Riemann manifolds, Nagoya Math. J. 15 (1959), 29–55. MR 108810
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 143-149
- MSC: Primary 53C35
- DOI: https://doi.org/10.1090/S0002-9939-1978-0503549-4
- MathSciNet review: 503549