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It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. Volume 2 continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":50509337690385,"sku":"NGR9780470555583","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51187359809809,"sku":"NIN9780470555583","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0470555580.jpg?v=1779962647"},{"product_id":"differential-geometry-of-curves-and-surfaces-book-shoshichi-kobayashi-9789811517389","title":"Differential Geometry of Curves and Surfaces","description":"This book is a posthumous publication of a classic by Prof. Shoshichi Kobayashi, who taught at U.C. Berkeley for 50 years, recently translated by Eriko Shinozaki Nagumo and Makiko Sumi Tanaka.     There are five chapters: 1. Plane Curves and Space Curves; 2. Local Theory of Surfaces in Space; 3. Geometry of Surfaces; 4. Gauss–Bonnet Theorem; and 5. Minimal Surfaces.     Chapter 1 discusses local and global properties of planar curves and curves in space. Chapter 2 deals with local properties of surfaces in 3-dimensional Euclidean space. Two types of curvatures — the Gaussian curvature K and the mean curvature H —are introduced.  The method of the moving frames, a standard technique in differential geometry, is introduced in the context of a surface in 3-dimensional Euclidean space.  In Chapter 3, the Riemannian metric on a surface is introduced and properties determined only by the first fundamental form are discussed. The concept of a geodesic introduced in Chapter 2 is extensively discussed, and several examples of geodesics are presented with illustrations. Chapter 4 starts with a simple and elegant proof of Stokes’ theorem for a domain.  Then the Gauss–Bonnet theorem, the major topic of this book, is discussed at great length. The theorem is a most beautiful and deep result in differential geometry. It yields a relation between the integral of the Gaussian curvature over a given oriented closed surface S and the topology of S in terms of its Euler number χ(S). Here again, many illustrations are provided to facilitate the reader’s understanding. Chapter 5, Minimal Surfaces, requires some elementary knowledge of complex analysis.  However, the author retained the introductory nature of this book and focused on detailed explanations of the examples of minimal surfaces given in Chapter 2.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":50791397327121,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50791398113553,"sku":"GOR014074205","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52433004429585,"sku":"NLS9789811517389","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52763963359505,"sku":"NIN9789811517389","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/981151738X.jpg?v=1751129672"},{"product_id":"foundations-of-differential-geometry-volume-2-book-shoshichi-kobayashi-9780471157328","title":"Foundations of Differential Geometry, Volume 2","description":"This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. 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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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52147323961617,"sku":"NLS9783540586593","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540586593.jpg?v=1757600170"},{"product_id":"hyperbolic-complex-spaces-book-shoshichi-kobayashi-9783540635345","title":"Hyperbolic Complex Spaces","description":"In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Caratheodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52333250707729,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52333251297553,"sku":"NLS9783540635345","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540635345.jpg?v=1758154166"},{"product_id":"hyperbolic-complex-spaces-book-shoshichi-kobayashi-9783642083396","title":"Hyperbolic Complex Spaces","description":"In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Caratheodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52476471836945,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52476472885521,"sku":"NLS9783642083396","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642083396.jpg?v=1759844117"},{"product_id":"hyperbolic-manifolds-and-holomorphic-mappings-an-introduction-book-shoshichi-kobayashi-9789812564962","title":"Hyperbolic Manifolds And Holomorphic Mappings: An Introduction","description":"The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections invariant metrics and pseudo-distances and hyperbolic complex manifolds within the section holomorphic mappings. The invariant distance introduced in the first edition is now called the Kobayashi distance, and the hyperbolicity in the sense of this book is called the Kobayashi hyperbolicity to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52663444504849,"sku":"NLS9789812564962","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789812564962.jpg?v=1762272049"},{"product_id":"hyperbolic-manifolds-and-holomorphic-mappings-an-introduction-book-shoshichi-kobayashi-9789812565891","title":"Hyperbolic Manifolds And Holomorphic Mappings: An Introduction","description":"The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections invariant metrics and pseudo-distances and hyperbolic complex manifolds within the section holomorphic mappings. 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This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics.  Originally published in 1987.  The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. 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