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- W4254172001 abstract "Publisher SummaryThis chapter discusses the symmetric spaces of the compact type. There are several Riemannian globally symmetric spaces U/K associated with the orthogonal symmetric Lie algebra of the compact type. These spaces are finite in number and have the same universal covering space. They are all described by means of the center of the universal covering group of U. The maximal abelian subspace, together with the root system, define the diagram D(U,K), in which certain information about the space U/K is contained, for example, the location of its conjugate points. Elementary properties of the Weyl group W(U,K) and the diagram are discussed in the chapter and the classification of the spaces U/K uses description of the fundamental group of U in terms of u. The singular set in U interferes and a proof of the fact that the singular set has no influence on the fundamental group utilizes some tools from the dimension theory, discussed in the chapter." @default.
- W4254172001 created "2022-05-12" @default.
- W4254172001 date "1962-01-01" @default.
- W4254172001 modified "2023-10-16" @default.
- W4254172001 title "Chapter VII Symmetric spaces of the compact Type" @default.
- W4254172001 doi "https://doi.org/10.1016/s0079-8169(08)62652-5" @default.
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