Elementary geometry provides the foundation of modern geometry. For the most part, the standard introductions end at the formal Euclidean geometry of high school. This book revisits geometry, but from the higher viewpoint of university mathematics. It is s

For a Riemannian manifold M, the geometry, topology and analysis are interrelated in ways that have become widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold. The eigenvalues of the Laplacian are naturally linked to the geometry of the manifold. For manifolds that admit spin structures, one obtains further information from equations involving Dirac operators and spinor fields. In the case of four-manifolds, for example, one has the remarkable Seiberg-Witten invariants.

Devoted to differential forms and their applications in various areas of mathematics and physics, this introductory textbook has plenty of examples and originated from courses on geometry and analysis. It presents a widely used mathematical technique in a lucid and readable style, introducing readers to the world of differential forms while covering relevant topics from analysis, differential geometry and mathematical physics.

Dieses Lehrbuch eignet sich als Fortsetzungskurs in Analysis nach den Grundvorlesungen im ersten Studienjahr. Die Vektoranalysis ist ein klassisches Teilgebiet der Mathematik mit vielfaltigen Anwendungen, zum Beispiel in der Physik. Das Buch fuhrt die Studierenden in die Welt der Differentialformen und Analysis auf Untermannigfaltigkeiten des Rn ein. Teile des Buches konnen auch sehr gut fur Vorlesungen in Differentialgeometrie oder Mathematischer Physik verwendet werden. Der Text enthalt viele ausfuhrliche Beispiele mit vollstandigem Losungsweg, die zur Ubung hilfreich sind. Zahlreiche...