ENGLISH

Differential Geometry: From Elastic Curves to Willmore Surfaces (Compact Textbooks in Mathematics)

By Ulrich Pinkall , Oliver Gross

Book information

Publisher
Birkhäuser
Year
2024
ISBN
3031398378, 9783031398377
Language
english
Format
PDF
Filesize
5 MB (4733913 bytes)
Edition
2024
Pages
214\206
Time added
2024-04-23 06:31:35

Description

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.

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