Abstract
A Riemannian manifold M is called weakly symmetric, if for any two points p and q in M, there exists an isometry f of M which interchanges p and q. An equivalent condition is that for every geodesic γ(t) in M, there exists an isometryfwhich reverses the geodesic, i. e.f(γ(t)) = γ(-t). A Riemannian symmetric space is clearly weakly symmetric. These manifolds were first studied by A.Selberg [S] who showed that for a weakly symmetric space, the algebra of isometry invariant differential operators is commutative.
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© 1996 Birkhäuser Boston
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Ziller, W. (1996). Weakly Symmetric Spaces. In: Gindikin, S. (eds) Topics in Geometry. Progress in Nonlinear Differential Equations and Their Applications, vol 20. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2432-7_15
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DOI: https://doi.org/10.1007/978-1-4612-2432-7_15
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