Differential Geometry : Curves - Surfaces - Manifolds

From a review of the German edition: The book covers all the topics which could be necessary later for learning higher level differential geometry. The material is very carefully sorted and easy-to-read. --Mathematical Reviews 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. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces, and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. For the second edition, a number of errors were corrected and some text and a number of figures have been added. The prerequisites are undergraduate analysis and linear algebra.