Geometry of weakly symmetric spaces
نویسندگان
چکیده
منابع مشابه
Geometry Of Weakly Symmetric Spaces
Weakly symmetric spaces are particular Riemannian homogeneous spaces which have been introduced by Selberg [21] in 1956 in the framework of his trace formula. They attracted only little interest until the author and Vanhecke [7] found a simple geometric characterization of weakly symmetric spaces which lead to a large number of new examples. The purpose of this note is to present a survey about...
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In this paper, new examples of weakly symmetric spaces in the sense of A. Selberg 14] are constructed. Let G be a connected, simply-connected, simple Lie group of hermitian type and K a maximal compactly embedded subgroup of G such that D = G=K is an irreducible classical bounded symmetric domain. Let G 1 and D 1 be circle extensions of G and D, respectively. The factor of automorphy induces a ...
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Symmetric spaces in the sense of E. Cartan supply major examples in Riemannian geometry. The study of their structure is connected closely to the theory of Lie groups. On these spaces, global analysis, particularly integration theory and theory of partial differential operators, arises in a canonical fashion by the requirement of geometric invariance. On R these two subjects are related to one ...
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Let (G,H) be a spherical pair and assume that G is a connected compact simple Lie group and H a closed subgroup of G. We prove in this paper that the homogeneous manifold G/H is weakly symmetric with respect to G and possibly an additional fixed isometry μ. It follows that M. Krämer’s classification list of such spherical pairs also becomes a classification list of compact weakly symmetric spac...
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1120 NOTICES OF THE AMS VOLUME 42, NUMBER 10 M any of the geometric objects of interest to number theorists arise as quotients of classical symmetric spaces by discrete subgroups of Lie groups. For example, the Riemann surfaces known as “modular curves”, which play a central role in Wiles’s proof of Fermat’s Last Theorem, are the quotients of the upper half plane by certain arithmetically defin...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1996
ISSN: 0025-5645
DOI: 10.2969/jmsj/04840745