Transformation Groups in Differential Geometry PDF
by Shoshichi Kobayashi
Part of the Classics in Mathematics series
Description
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.
Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Springer Berlin Heidelberg
- Publication Date:06/12/2012
- Category:
- ISBN:9783642619816
Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Springer Berlin Heidelberg
- Publication Date:06/12/2012
- Category:
- ISBN:9783642619816
