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.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
N = 8 gaugings revisited: an exhaustive classification
Francesco Cordaro,Francesco Cordaro,Pietro Fré,Pietro Fré,Leonardo Gualtieri,Leonardo Gualtieri,P. Termonia,P. Termonia,Mario Trigiante +8 more
TL;DR: In this paper, the authors consider the problem of gauging the most general electric subgroup and show that admissible theories are fully characterized by a single algebraic equation to be satisfied by the embedding Ggauge → SL(8, R) ⊂ E7(7).
107
A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates
Guillermo Gallego,Anthony Yezzi +1 more
TL;DR: A compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates is presented to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.
Cyclic coverings, Calabi-Yau manifolds and Complex multiplication
TL;DR: In this article, the authors constructed families of Calabi-Yau manifolds with dense set of complex multiplication fibers in an arbitrary dimension and studied the generic Hodge groups of families of cyclic covers of the projective line.
The Addition Formula for Jacobi Polynomials and Spherical Harmonics
TL;DR: In this paper, a new algebraic proof using spherical harmonics was presented, where Gegenbauer's addition formula was generalized for Jacobi polynomials by an algebraic approach (cf. the author's paper in [10]).
105