Transformation Groups in Differential Geometry [electronic resource] /

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.

Bibliographic Details

Main Authors:	Kobayashi, Shoshichi. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Berlin, Heidelberg : Springer Berlin Heidelberg, 1995
Subjects:	Mathematics., Group theory., Differential geometry., Differential Geometry., Group Theory and Generalizations.,
Online Access:	http://dx.doi.org/10.1007/978-3-642-61981-6
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