| Transformation Groups in Differential Geometry 1995 Edition Contributor(s): Kobayashi, Shoshichi (Author) |
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ISBN: 3540586598 ISBN-13: 9783540586593 Publisher: Springer OUR PRICE: $56.99 Product Type: Paperback - Other Formats Published: February 1995 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Algebra - Abstract |
| Dewey: 516.36 |
| LCCN: 94041257 |
| Series: Classics in Mathematics |
| Physical Information: 0.41" H x 6.14" W x 9.21" (0.61 lbs) 182 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |