This is a translation of an introductory text based on a lecture series delivered by the renowned differential geometer, Professor S.S. Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, sought to combine simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fibre bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specifically for this edition by Professor Chern to bring the text into perspective.
Weihuan Chen (Peking Univ China)
, Shiing-shen Chern (Nankai Univ
, Kai S Lam (California State Polytechnic Univ
, K.S. Lam (California State Polytechnic University
Country of Publication:
Series: Series On University Mathematics
15 November 1999
Professional and scholarly
Professional & Vocational
A / AS level
Further / Higher Education
Differentiable manifolds; multilinear algebra; exterior differential calculus; connections; Riemannian geometry; Lie groups and moving frames; complex manifolds; Finsler geometry; historical notes; differential geometry and theoretical physics.