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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
Finiteness of the family of rational and meromorphic mappings into algebraic varieties
Junjiro Noguchi,Toshikazu Sunada +1 more
TL;DR: In this paper, the authors considered the case where the mappings are not necessarily dominant and proved that there are only a finite number of dominant meromorphic mappings onto a complex space of general type, and its algebraic proof which covers the positive characteristic case was given by [14] (cf.
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Vanishing theorems for lie algebra cohomology and the cohomology of discrete subgroups of semisimple lie groups
TL;DR: In this article, the authors present a new proof of a recent vanishing theorem of Borel and Wallach [6] and Zuckerman [34] about the cohomology groups of a connected semisimple Lie group with finite center.
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Spherical functions and integral geometry
TL;DR: In this article, the authors present two proofs of an integral geometric formula concerning n-dimensional ellipsoids, based on a representation theorem for spherical functions due to Harish-Chandra.
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•Posted Content
Division Algebras and Non-Commensurable Isospectral Manifolds
TL;DR: In this paper, it was shown that for d ≥ 3 and S = PGLd (R)/POd(R), or S = pGLd(C)/PUd (C), the situation is quite different: there are arbitrarily large finite families of isospectral non-commensurable compact manifolds covered by S. Reid (R).
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