Differential Forms and Applications (Universitext)

The book treats differential forms and uses them to study some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely the Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames of E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. Everything is then put together in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.

• Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)
• Riemannian Geometry
• Differential Topology
• An Introduction to Manifolds: Second Edition (Universitext)
• Differential Geometry: Connections, Curvature, and Characteristic Classes (Graduate Texts in Mathematics)
• Emmy Noether's Wonderful Theorem
• Differential Forms and Connections
• Geometric Mechanics - Part I: Dynamics And Symmetry (2Nd Edition)
• Geometric Mechanics - Part Ii: Rotating, Translating And Rolling (2Nd Edition)
• Advanced Calculus (Dover Books on Mathematics)