Description
Book SynopsisOffers an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples.
Trade ReviewThe book provides an excellent introduction to the differential geometry of curves, surfaces and Riemannian manifolds that should be accessible to a variety of readers… Frankly, this is a great book… even after only two chapters the reader is exposed to a lot of interesting mathematics. If you are looking to teach or learn differential geometry at an introductory level,
Differential Geometry Curves—Surfaces—Manifolds is a great resource to have on hand." - Jason M. Graham,
MAA ReviewsTable of Contents
- Notations and prerequisites from analysis
- Curves in $\mathbb{R}^n$
- The local theory of surfaces
- The intrinsic geometry of surfaces
- Riemannian manifolds
- The curvature tensor
- Spaces of constant curvature
- Einstein spaces
- Solutions to selected exercises
- Bibliography
- List of notation
- Index
