Author : Shoshichi Kobayashi
Release : 2012-12-06
Genre : Mathematics
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Book Rating : 819/5 ( reviews)

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Transformation Groups in Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Transformation Groups in Differential Geometry write by Shoshichi Kobayashi. This book was released on 2012-12-06. Transformation Groups in Differential Geometry available in PDF, EPUB and Kindle. 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.