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Transformation groups in differential geometry

Author: Shoshichi Kobayashi
Publisher: Berlin ; New York : Springer, 1972, ©1995.
Series: Springer classics in mathematics.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:

This text, part of the "Springer Classics in Mathematics" series, looks at transformation groups in differential geometry.

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Document Type: Book
All Authors / Contributors: Shoshichi Kobayashi
ISBN: 3540586598 9783540586593
OCLC Number: 31374337
Description: viii, 182 pages : illustrations ; 24 cm.
Contents: 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-Kahler Manifolds.- 6. Compact Kahler Manifolds with Constant Scalar Curvature.- 7. Conformal Changes of the Laplacian.- 8. Compact Kahler 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.
Series Title: Springer classics in mathematics.
Responsibility: S. Kobayashi.
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