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: Pinkall, Ulrich, Gross, Oliver
Materialtyp: Online
Språk:engelska
Utgiven: Springer Nature 2024
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Länkar:ONIX_20240313_9783031398384_13
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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
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publisher Springer Nature
publisherStr Springer Nature
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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