Open AccessBook
Differential Geometry and Symmetric Spaces
Sigurdur Helgason
- 01 Jan 1962
TL;DR: In this article, the classification of symmetric spaces has been studied in the context of Lie groups and Lie algebras, and a list of notational conventions has been proposed.
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Abstract: Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric spaces of the compact type Hermitian symmetric spaces On the classification of symmetric spaces Functions on symmetric spaces Bibliography List of notational conventions Symbols frequently used Author index Subject index Reviews for the first edition.
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Citations
Biharmonic hypersurfaces in a Riemannian manifold with non-positive Ricci curvature
TL;DR: In this paper, it was shown that for a bi-harmonic hypersurface (M, g) of a Riemannian manifold (N, h) of non-positive Ricci curvature, if
69
Du côté de chez Pu
TL;DR: Gauthier-Villars as discussed by the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).
Discrete Nonholonomic LL Systems on Lie Groups
Yuri N. Fedorov,Dmitry V. Zenkov +1 more
TL;DR: In this paper, the discrete Euler-Lagrange equations are reduced to the discrete euler-Poincare-Suslov equations and the dynamics associated with these equations are shown to evolve on a subvariety of the Lie group G. The theory is illustrated with two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh.
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On the Nature of Quantum Geometry
Roger Penrose
- 01 Jan 1972
TL;DR: In this article, the authors discuss the fundamental role played by the mathematical concept of continuum in virtually the whole of accepted present-day physical theory, including quantum theory, in the development of several of the thoughts which are expressed here.