Differential Geometry

From Elastic Curves to Willmore Surfaces

von Ulrich Pinkall, Oliver Gross

203 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

This open access book covers the main topics for a course on the differential geometry of curves and surfaces. Unlike the common approach in existing textbooks, there is a strong focus on variational problems, ranging from elastic curves to surfaces that minimize area, or the Willmore functional. Moreover, emphasis is given on topics that are useful for applications in science and computer graphics. Most often these applications are concerned with finding the shape of a curve or a surface that minimizes physically meaningful energy. Manifolds are not introduced as such, but the presented approach provides preparation and motivation for a follow-up course on manifolds, and topics like the Gauss-Bonnet theorem for compact surfaces are covered.

• Reihe: Compact Textbooks in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Geometrie Differentielle und Riemannsche Geometrie
• ISBN: 9783031398377
• Sprache: Englisch
• Erscheinungsdatum: 14.02.2024
• Größe: 23.5 x 15.5 cm
• Verlag: Springer International Publishing