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Differential Geometry
Ulrich PinkallOliver Gross
其他書名
From Elastic Curves to Wilmore Surfaces
出版Springer International Publishing AG, 2024
ISBN30313983869783031398384
URLhttp://books.google.com.hk/books?id=cx_A0AEACAAJ&hl=&source=gbs_api
註釋Zusammenfassung: 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