Lie groups and geometric aspects of isometric actions / Marcos M. Alexandrino y Renato G Bettiol
Editor: New York, NY : Springer Science+Business Media, 2015Descripción: 218 pages ; 24cmTipo de contenido: text Tipo de medio: unmediated Tipo de portador: volumeISBN: 9783319166124Otra clasificación: 22-01 (22E46 22F05 53-01) Recursos en línea: Table of contents only | Publisher description | Contributor biographical informationPart I Lie Groups -- 1 Basic Results on Lie Groups [3] -- 1.1 Lie Groups and Lie Algebras [3] -- 1.2 Lie Subgroups and Lie Homomorphisms -- 1.3 Exponential Map and Adjoint Representation [13] -- 1.4 Closed Subgroups and More Examples [18] -- 2 Lie Groups with Bi-invariant Metrics [27] -- 2.1 Basic Facts of Riemannian Geometry [27] -- 2.2 Bi-invariant Metrics [38] -- 2.3 Killing Form and Semisimple Lie Algebras [41] -- 2.4 Splitting Lie Groups with Bi-invariant Metrics [45] -- Part II Isometric Actions -- 3 Proper and Isometric Actions [51] -- 3.1 Proper Actions and Fiber Bundles [51] -- 3.2 Slices and Tubular Neighborhoods [64] -- 3.3 Isometric Actions [69] -- 3.4 Principal Orbits [73] -- 3.5 Orbit Types [76] -- 4 Adjoint and Conjugation Actions [85] -- 4.1 Maximal Tori and Polar Actions [85] -- 4.2 Normal Slices of Conjugation Actions [92] -- 4.3 Roots of a Compact Lie Group [93] -- 4.4 Weyl Group [99] -- 4.5 Dynkin Diagrams [102] -- 5 Polar Foliations [109] -- 5.1 Definitions and First Examples [109] -- 5.2 Holonomy and Orbifolds [111] -- 5.3 Surgery and Suspension of Homomorphisms [116] -- 5.4 Differential and Geometric Aspects of Polar Foliations [117] -- 5.5 Transnormal and Isoparametric Maps [126] -- 5.6 Perspectives [135] -- 6 Low Cohomogeneity Actions and Positive Curvature [139] -- 6.1 Cheeger Deformation [139] -- 6.2 Compact Homogeneous Spaces [145] -- 6.3 Cohomogeneity One Actions [157] -- 6.4 Positive and Nonnegative Curvature via Symmetries [171] -- A Rudiments of Smooth Manifolds [185] -- A.l Smooth Manifolds [185] -- A.2 Vector Fields [187] -- A.3 Foliations and the Frobenius Theorem [190] -- A.4 Differential Forms, Integration, and de Rham Cohomology [192] -- References [199] -- Index [209] --
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
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Instituto de Matemática, CONICET-UNS | Últimas adquisiciones | 22 Al382 (Browse shelf) | Available | A-9390 |
Browsing Instituto de Matemática, CONICET-UNS shelves, Shelving location: Últimas adquisiciones Close shelf browser
| 16 R128 Hopf algebras / | 18 L821 Algebraic operads / | 20 G892 A journey through representation theory : from finite groups to Quivers via Algebras / | 22 Al382 Lie groups and geometric aspects of isometric actions / | 22 B491-2 Lie groups / | 22 D875 Lie groups / | 22 H288 Harmonic analysis on semi-simple Lie groups. |
Part I Lie Groups --
1 Basic Results on Lie Groups [3] --
1.1 Lie Groups and Lie Algebras [3] --
1.2 Lie Subgroups and Lie Homomorphisms --
1.3 Exponential Map and Adjoint Representation [13] --
1.4 Closed Subgroups and More Examples [18] --
2 Lie Groups with Bi-invariant Metrics [27] --
2.1 Basic Facts of Riemannian Geometry [27] --
2.2 Bi-invariant Metrics [38] --
2.3 Killing Form and Semisimple Lie Algebras [41] --
2.4 Splitting Lie Groups with Bi-invariant Metrics [45] --
Part II Isometric Actions --
3 Proper and Isometric Actions [51] --
3.1 Proper Actions and Fiber Bundles [51] --
3.2 Slices and Tubular Neighborhoods [64] --
3.3 Isometric Actions [69] --
3.4 Principal Orbits [73] --
3.5 Orbit Types [76] --
4 Adjoint and Conjugation Actions [85] --
4.1 Maximal Tori and Polar Actions [85] --
4.2 Normal Slices of Conjugation Actions [92] --
4.3 Roots of a Compact Lie Group [93] --
4.4 Weyl Group [99] --
4.5 Dynkin Diagrams [102] --
5 Polar Foliations [109] --
5.1 Definitions and First Examples [109] --
5.2 Holonomy and Orbifolds [111] --
5.3 Surgery and Suspension of Homomorphisms [116] --
5.4 Differential and Geometric Aspects of Polar Foliations [117] --
5.5 Transnormal and Isoparametric Maps [126] --
5.6 Perspectives [135] --
6 Low Cohomogeneity Actions and Positive Curvature [139] --
6.1 Cheeger Deformation [139] --
6.2 Compact Homogeneous Spaces [145] --
6.3 Cohomogeneity One Actions [157] --
6.4 Positive and Nonnegative Curvature via Symmetries [171] --
A Rudiments of Smooth Manifolds [185] --
A.l Smooth Manifolds [185] --
A.2 Vector Fields [187] --
A.3 Foliations and the Frobenius Theorem [190] --
A.4 Differential Forms, Integration, and de Rham Cohomology [192] --
References [199] --
Index [209] --
MR, REVIEW #
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