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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
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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?)

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  • [2] R. Gandulfo and J. Tirao, Multiplier transformations of functions on compact two-point homogeneous spaces, Trabalhos de Matemática 126 (1977).
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Keywords: Geodesic symmetry, semisimple Lie group, involutive automorphism, restricted root, projective spaces
Article copyright: © Copyright 1978 American Mathematical Society