Differential Geometry
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. Mo...
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| Huvudupphov: | , |
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| Materialtyp: | Online |
| Språk: | engelska |
| Utgiven: |
Springer Nature
2024
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| Ämnen: | |
| Länkar: | ONIX_20240313_9783031398384_13 |
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| _version_ | 1869525674443669504 |
|---|---|
| author | Pinkall, Ulrich Gross, Oliver |
| author_browse | Gross, Oliver Pinkall, Ulrich |
| author_facet | Pinkall, Ulrich Gross, Oliver |
| author_sort | Pinkall, Ulrich |
| collection | Directory of Open Access Books |
| 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. |
| format | Online |
| id | doab-20.500.12854ir-135570 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1355702025-07-18T09:46:31Z Differential Geometry Pinkall, Ulrich Gross, Oliver Differential Geometry Surfaces Curves Elastic Minimal Willmore Variational Calculus Riemannian Geometry Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry 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. 2024-03-14T04:07:54Z 2024-03-14T04:07:54Z 2024-03-13T11:09:58Z 2024 book ONIX_20240313_9783031398384_13 OCN: 1423523829 https://library.oapen.org/handle/20.500.12657/88305 9783031398384 9783031398377 https://directory.doabooks.org/handle/20.500.12854/135570 eng Compact Textbooks in Mathematics open access image/jpeg image/jpeg image/jpeg image/jpeg image/jpeg n/a n/a n/a n/a n/a https://library.oapen.org/bitstream/20.500.12657/88305/1/978-3-031-39838-4.pdf https://library.oapen.org/bitstream/20.500.12657/88305/1/978-3-031-39838-4.pdf https://library.oapen.org/bitstream/20.500.12657/88305/1/978-3-031-39838-4.pdf https://library.oapen.org/bitstream/20.500.12657/88305/1/978-3-031-39838-4.pdf https://library.oapen.org/bitstream/20.500.12657/88305/1/978-3-031-39838-4.pdf Springer Nature Birkhäuser 10.1007/978-3-031-39838-4 10.1007/978-3-031-39838-4 9fa3421d-f917-4153-b9ab-fc337c396b5a Deutsche Forschungsgemeinschaft Technische Universität Berlin 3358520f-7ab2-42ab-80ef-88a2dbe6a901 f5e85b6c-dd8b-4bb3-a493-22723c79d368 9783031398384 9783031398377 DFG - German Research Foundation Birkhäuser 203 Cham [...] [...] open access |
| spellingShingle | Differential Geometry Surfaces Curves Elastic Minimal Willmore Variational Calculus Riemannian Geometry Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry Pinkall, Ulrich Gross, Oliver Differential Geometry |
| title | Differential Geometry |
| title_full | Differential Geometry |
| title_fullStr | Differential Geometry |
| title_full_unstemmed | Differential Geometry |
| title_short | Differential Geometry |
| title_sort | differential geometry |
| topic | Differential Geometry Surfaces Curves Elastic Minimal Willmore Variational Calculus Riemannian Geometry Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry |
| topic_facet | Differential Geometry Surfaces Curves Elastic Minimal Willmore Variational Calculus Riemannian Geometry Textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry thema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometry |
| url | ONIX_20240313_9783031398384_13 |
| work_keys_str_mv | AT pinkallulrich differentialgeometry AT grossoliver differentialgeometry |