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Differential Geometry

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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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Publisher

: Springer Cham., 2024

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Language

English

ISBN/ISSN

978-3-031-39837-7

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NONE

Content Type

text

Media Type

computer

Carrier Type

online resource

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Cataloger

hasyim

Source

https://doi.org/10.1007/978-3-031-39838-4

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hasyim

Digital Object Identifier (DOI)

https://doi.org/10.1007/978-3-031-39838-4

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