Differential Geometry : From Elastic Curves to Willmore Surfaces
Book Details
Format
Paperback / Softback
Book Series
Compact Textbooks in Mathematics
ISBN-10
3031398378
ISBN-13
9783031398377
Publisher
Birkhauser Verlag AG
Imprint
Birkhauser Verlag AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Feb 14th, 2024
Print length
203 Pages
Product Classification:
Differential & Riemannian geometryDifferential and Riemannian geometry
Ksh 8,100.00
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This open access book covers the main topics for a course on the differential geometry of curves and surfaces. 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.
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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