Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Antipodal manifolds in compact symmetric spaces of rank one

Author: Juan Alfredo Tirao
Journal: Proc. Amer. Math. Soc. 72 (1978), 143-149
MSC: Primary 53C35
MathSciNet review: 503549
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] É. Cartan, Sur certaines formes riemannienes remarquables des géométries a groupe fondamental simple, Ann. Sci. École Norm. Sup. 44 (1927), 345-467.
  • [2] R. Gandulfo and J. Tirao, Multiplier transformations of functions on compact two-point homogeneous spaces, Trabalhos de Matemática 126 (1977).
  • [3] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962. MR 0145455 (26:2986)
  • [4] -, The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math. 113 (1965), 153-180. MR 0172311 (30:2530)
  • [5] T. Nagano, Homogeneous sphere bundles and the isotropic Riemannian manifolds, Nagoya Math. J. 15 (1959), 29-55. MR 0108810 (21:7522)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C35

Retrieve articles in all journals with MSC: 53C35

Additional Information

Keywords: Geodesic symmetry, semisimple Lie group, involutive automorphism, restricted root, projective spaces
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society