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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. 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. The
second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.
List of contents
Submanifolds.
Variations of the Length Integral.
Complex Manifolds.
Homogeneous Spaces.
Symmetric Spaces.
Characteristic Classes.
Appendices.
Notes.
Bibliography.
Summary of Basic Notations.
Index.
About the author
Shoshichi Kobayashi was born January 4, 1932 in Kofu, Japan. After obtaining his mathematics degree from the University of Tokyo and his Ph.D. from the University of Washington, Seattle, he held positions at the Institute for Advanced Study, Princeton, at MIT and at the University of British Columbia between 1956 and 1962, and then moved to the University of California, Berkeley, where he is now Professor in the Graduate School.
Kobayashi's research spans the areas of differential geometry of real and complex variables, and his numerous resulting publications include several book:
Foundations of Differential Geometry with
K. Nomizu,
Hyperbolic Complex Manifolds and Holomorphic Mappings and
Differential Geometry of Complex Vector Bundles.
Summary
One of two volumes which lay the foundations for understanding differential geometry. This work familiarizes readers with various techniques of computation.
