Analogues of the Beltrami–Klein Model for Rank One Symmetric Spaces of Noncompact Type
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Rank one symmetric spaces of noncompact type are studied from the point of view of realizations. Models for these spaces as domains in Euclidean spaces are discussed. Calculations in the text are given as explicit as possible. Presented are explicit formulas for the Riemannian measure, the Laplace–Beltrami operator, the symmetries, the distance, and so on. The exposition differs from the existing books. The presented material gives an alternative way to learn about and work on symmetric spaces.
KeywordsSymmetric Space Sectional Curvature Hyperbolic Space Complete Riemannian Manifold Constant Sectional Curvature
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