Differential Geometry From Elastic Curves to Willmore Surfaces /
Pinkall, Ulrich.
Differential Geometry From Elastic Curves to Willmore Surfaces / [electronic resource] : by Ulrich Pinkall, Oliver Gross. - 1st ed. 2024. - XI, 203 p. 80 illus., 66 illus. in color. online resource. - Compact Textbooks in Mathematics, 2296-455X . - Compact Textbooks in Mathematics, .
Open Access
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.
9783031398384
10.1007/978-3-031-39838-4 doi
Geometry, Differential.
Differential Geometry.
QA641-670
516.36
Differential Geometry From Elastic Curves to Willmore Surfaces / [electronic resource] : by Ulrich Pinkall, Oliver Gross. - 1st ed. 2024. - XI, 203 p. 80 illus., 66 illus. in color. online resource. - Compact Textbooks in Mathematics, 2296-455X . - Compact Textbooks in Mathematics, .
Open Access
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.
9783031398384
10.1007/978-3-031-39838-4 doi
Geometry, Differential.
Differential Geometry.
QA641-670
516.36