| Dewey Class |
516.36 |
| Titel |
Transformation Groups in Differential Geometry ([EBook]) / by Shoshichi Kobayashi. |
| Verfasser |
Kobayashi, Shoshichi , 1932- |
| Other name(s) |
SpringerLink (Online service) |
| Veröffentl |
Berlin, Heidelberg : Springer , 1995. |
| Physical Details |
VIII, 182 pages : online resource. |
| Reihe |
Classics in mathematics 0071-1136 ; ; 70 |
| ISBN |
9783642619816 |
| Summary Note |
Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.: |
| Contents note |
I. Automorphisms of G-Structures -- 1. G -Structures -- 2. Examples of G-Structures -- 3. Two Theorems on Differentiable Transformation Groups -- 4. Automorphisms of Compact Elliptic Structures -- 5. Prolongations of G-Structures -- 6. Volume Elements and Symplectic Structures -- 7. Contact Structures -- 8. Pseudogroup Structures, G-Structures and Filtered Lie Algebras -- II. Isometries of Riemannian Manifolds -- 1. The Group of Isometries of a Riemannian Manifold -- 2. Infinitesimal Isometries and Infinitesimal Affine Transformations -- 3. Riemannian Manifolds with Large Group of Isometries -- 4. Riemannian Manifolds with Little Isometries -- 5. Fixed Points of Isometries -- 6. Infinitesimal Isometries and Characteristic Numbers -- III. Automorphisms of Complex Manifolds -- 1. The Group of Automorphisms of a Complex Manifold -- 2. Compact Complex Manifolds with Finite Automorphism Groups -- 3. Holomorphic Vector Fields and Holomorphic 1-Forms -- 4. Holomorphic Vector Fields on Kahler Manifolds -- 5. Compact Einstein-Kähler Manifolds -- 6. Compact Kähler Manifolds with Constant Scalar Curvature -- 7. Conformal Changes of the Laplacian -- 8. Compact Kähler Manifolds with Nonpositive First Chern Class -- 9. Projectively Induced Holomorphic Transformations -- 10. Zeros of Infinitesimal Isometries -- 11. Zeros of Holomorphic Vector Fields -- 12. Holomorphic Vector Fields and Characteristic Numbers -- IV. Affine, Conformal and Projective Transformations -- 1. The Group of Affine Transformations of an Affinely Connected Manifold -- 2. Affine Transformations of Riemannian Manifolds -- 3. Cartan Connections -- 4. Projective and Conformal Connections -- 5. Frames of Second Order -- 6. Projective and Conformal Structures -- 7. Projective and Conformal Equivalences -- Appendices -- 1. Reductions of 1-Forms and Closed 2-Forms -- 2. Some Integral Formulas -- 3. Laplacians in Local Coordinates. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-3-642-61981-6 |
| LINKS ZU 'VERWANDTEN WERKEN |
Schlagwörter: .
Differential Geometry .
Group theory .
Group Theory and Generalizations .
Mathematics .
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