Given a mathematical structure, one of the basic associated mathematicalobjects is its automorphism group. The object of this book is to give abiased account of automorphism groups of differential geometric struc-tures. All geometric structures are not created equal; some are creationsof sods while others are products of lesser human minds. Amongst theformer, Riemannian and complex structures stand out for their beautyand wealth. A major portion of this book is therefore devoted to thesetwo structures.

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 Sympleetic 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 Isometrics and Infinitesimal Affine Transformations

 3.Riemannian Manifolds with Large Group of Isometries

 4.Riemannian Manifolds with Little Isometrics

 5.Fixed Points of Isometrics

 6.Infinitesimal Isometrics and Characteristic Numbers

Ⅲ.Automorphisms of Complex Manifolds

 I.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.Holomorphie 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 Isometrics

 11.Zeros of Holomorphic Vector Fields

 12.Holomorphic Vector Fields and Characteristic Numbers

Ⅳ.A/fine, Conformal and Projective Transformations

 1.The Group of Affine Transformations of an A/finely 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 l-Forms and Closed 2-Forms

 2.Some Integral Formulas

 3.Laplacians in Local Coordinates

 4.A Remark on dd-Cohomology

Bibliography

Index