Differential Geometry
المؤلف: Louis Auslander
الناشر: Harper & Row
تاريخ النشر: 1967
عدد الصفحات: 271
امتداد الملف: Djvu
اللغة: الإنجليزية
ردمك-10: 0063560038
ردمك-13: 9780063560031
المؤلف: Louis Auslander
الناشر: Harper & Row
تاريخ النشر: 1967
عدد الصفحات: 271
امتداد الملف: Djvu
اللغة: الإنجليزية
ردمك-10: 0063560038
ردمك-13: 9780063560031
وصف الكتاب
In this book we have tried to give a treatment of the differential geometry of surfaces that combines both the modern and classical approaches to the subject. With this goal in mind, we have organized the book as follows: Chapters I and II are general in nature and treat the algebraic and analytic prerequisites for the modern approach to manifold theory. Chapter III treats matrix Lie groups and has as its goal the equations of structure of a matrix Lie group. We have chosen to treat matrix Lie groups rather than general Lie groups because we felt that the simplification of presentation possible in this concrete case is so great as to be worth the slight loss of generality. Chapters IV and V cover the local differential geometry of curves and surfaces. We have started with the modern approach in Chapter IV because we felt that it best motivates the basic definitions. In Chapter V we redo much of the work already covered in Chapter IV, but this time in a treatment that uses the affine connection and conveys theclassical approach to the subject and its method of computation. Chapters VI and VII serve as an introduction to the theory of Riemann manifolds. In Chapter VI we have presented a fairly complete account of the surfaces of constant curvature and hyperbolic geometry. In Chapter VII, we have contented ourselves with a brief introduction to the Gauss-Bonnet theorem.
In this book we have tried to give a treatment of the differential geometry of surfaces that combines both the modern and classical approaches to the subject. With this goal in mind, we have organized the book as follows: Chapters I and II are general in nature and treat the algebraic and analytic prerequisites for the modern approach to manifold theory. Chapter III treats matrix Lie groups and has as its goal the equations of structure of a matrix Lie group. We have chosen to treat matrix Lie groups rather than general Lie groups because we felt that the simplification of presentation possible in this concrete case is so great as to be worth the slight loss of generality. Chapters IV and V cover the local differential geometry of curves and surfaces. We have started with the modern approach in Chapter IV because we felt that it best motivates the basic definitions. In Chapter V we redo much of the work already covered in Chapter IV, but this time in a treatment that uses the affine connection and conveys theclassical approach to the subject and its method of computation. Chapters VI and VII serve as an introduction to the theory of Riemann manifolds. In Chapter VI we have presented a fairly complete account of the surfaces of constant curvature and hyperbolic geometry. In Chapter VII, we have contented ourselves with a brief introduction to the Gauss-Bonnet theorem.
