Lectures on differential geometry
Chern, S. S.
Lectures on differential geometry - Singapore: World Scientific, 2022 - x, 356p. pkb - Series on university mathematics Vol. 1 1793-1193 .
Contents:
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
This book is a translation of an authoritative 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, was a unique contribution to the mathematics literature, combining 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 fiber 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 specially for this edition by Professor Chern to bring the text into perspectives.
9781944659899
MATHEMATICS
DIFFERENTIAL GEOMETRY
ALGEBRA
MANIFOLDS
LIE GROUPS
514.7 / CHE-L
Lectures on differential geometry - Singapore: World Scientific, 2022 - x, 356p. pkb - Series on university mathematics Vol. 1 1793-1193 .
Contents:
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
This book is a translation of an authoritative 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, was a unique contribution to the mathematics literature, combining 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 fiber 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 specially for this edition by Professor Chern to bring the text into perspectives.
9781944659899
MATHEMATICS
DIFFERENTIAL GEOMETRY
ALGEBRA
MANIFOLDS
LIE GROUPS
514.7 / CHE-L
