<p>This volume covers local as well as global differential geometry of curves and surfaces.   </p>

Differential Geometry of Curves and Surfaces

Science & Math

Manfredo P. Do Carmo

Mathematics

PRENTICE/HALL

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 Forms and Applications (Universitext)

Springer

Motivation 101 (The Psych 101 Series)

Springer Publishing Company

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Eva-Maria Konig

Reclam Philipp Jun.

ABC of Pediatric Surgical Imaging

This is a new and expanded edition of this textbook for first-year graduate students in mathematics and physics, discussing the basic language of Riemannian geometry and presenting some of its most fundamental theorems. It is elementary in that it only assumes a modest background from the readers, making it suitable for a wide variety of students and course structures. It features basic definitions and theorems, examples and numerous exercises. The book begins with the definition of a differential manifold and ends with one of the most important results in Riemmanian geometry - a proof of the Sphere Theorem.

Riemannian Geometry (Mathematics: Theory and Applications)

Birkhauser

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Books by Manfredo P. Do Carmo