Transformation Groups in Differential Geometry

di Shoshichi Kobayashi (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 1995

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.

• Autore: Shoshichi Kobayashi
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Classics in Mathematics
• Anno: 1995
• Rilegatura: Paperback / softback
• Pagine: 182 p.
• Dimensioni: 233 x 155 mm
• Peso: 980 gr.
• EAN: 9783540586593

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