This carefully written book is 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. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and--as a new feature--a good number of solutions to selected exercises.
Rezensionen / Stimmen
The 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 Reviews
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Editions-Typ
Maße
Höhe: 216 mm
Breite: 140 mm
Gewicht
ISBN-13
978-1-4704-2320-9 (9781470423209)
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Schweitzer Klassifikation
Wolfgang Kuhnel, University of Stuttgart, Germany.
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
