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Differential Geometry
Ulrich Pinkall and Oliver Gross
2024
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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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Keywords
- Curves
- Differential Geometry
- elastic
- Minimal
- Riemannian geometry
- Surfaces
- Textbook
- thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry
- variational calculus
- Willmore
Links
DOI: 10.1007/978-3-031-39838-4Editions