From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices provide background information on point-set topology, calculus of
Differential Geometry of Manifolds, Second Edition, presents the extension of differential geometry from curves and surfaces to manifolds in general. The book provides a broad introduction to differentiable and Riemannian manifolds, tying together classical and modern formulations. It introduces manifolds in a streamlined and mathematically rigorous way while keeping a view toward applications, particularly in physics.


The author takes a practical approach, containing extensive exercises and focusing on applications, including the Hamiltonian formulations of mechanics, electromagnetism, and string theory.


The Second Edition of this successful textbook offers several notable points of revision.