Transformation Groups in Differential Geometry by Shoshichi Kobayashi
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.-
Introduction to Calculus and Analysis I
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Finite Geometries
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Elliptic Partial Differential Equations of Second Order
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Function Theory in the Unit Ball of Cn
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The Analysis of Linear Partial Differential Operators III
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Combinatorial Group Theory
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Algebraic Geometry I
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Complex Manifolds and Deformation of Complex Structures
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Geometric Measure Theory
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Multiple Integrals in the Calculus of Variations
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Number Theory
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Stability Theory of Dynamical Systems
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Lectures on Celestial Mechanics
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The Analysis of Linear Partial Differential Operators I
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Algebraic Surfaces
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Diffusion Processes and their Sample Paths
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Topological Methods in Algebraic Geometry
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C*-Algebras and W*-Algebras
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The Theory of Stochastic Processes II
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Combinatorial Theory
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The Theory of Stochastic Processes I
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Theory of Stein Spaces
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Homology
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The Theory of Stochastic Processes III
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An Introduction to the Geometry of Numbers
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Introduction to Calculus and Analysis II/2
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Introduction to Quadratic Forms
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Entropy, Large Deviations, and Statistical Mechanics
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Hamiltonian Methods in the Theory of Solitons
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Einstein Manifolds
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Classical Potential Theory and Its Probabilistic Counterpart
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K-Theory
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Algebraic Topology - Homotopy and Homology
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Problems and Theorems in Analysis I
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Probability in Banach Spaces
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The Analysis of Linear Partial Differential Operators IV
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Lectures on Algebraic Topology
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Problems and Theorems in Analysis II
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Interacting Particle Systems
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The Analysis of Linear Partial Differential Operators II
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Practical Quantum Mechanics
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Perturbation Theory for Linear Operators
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Introduction to Calculus and Analysis II/1
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Functional Analysis
Biography of Shoshichi Kobayashi
Shoshichi Kobayashi was born January 4, 1932 in Kofu, Japan. After obtaining his mathematics degree from the University of Tokyo and his Ph.D. from the University of Washington, Seattle, he held positions at the Institute for Advanced Study, Princeton, at MIT and at the University of British Columbia between 1956 and 1962, and then moved to the University of California, Berkeley, where he is now Professor in the Graduate School.
Kobayashi's research spans the areas of differential geometry of real and complex variables, and his numerous resulting publications include several book: Foundations of Differential Geometry with N. Nomizu, Hyperbolic Complex Manifolds and Holomorphic mappings and Differential Geometry of Complex Vector Bundles.
| SKU | Unavailable |
| ISBN 13 | 9783540586593 |
| ISBN 10 | 3540586598 |
| Title | Transformation Groups in Differential Geometry |
| Author | Shoshichi Kobayashi |
| Series | Classics In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 1995-02-15 |
| Number of pages | 182 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |