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Cover: 9783031398377 | Differential Geometry | From Elastic Curves to Willmore Surfaces | xi
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Differential Geometry
From Elastic Curves to Willmore Surfaces
Taschenbuch von Oliver Gross (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
Ulrich Pinkall was born in 1955. In 1979 he graduated in Mathematics and Physics at the University of Freiburg, where in 1981 he also got his PhD in Mathematics. From 1984 to 1986 he worked at the MPI für Mathematik in Bonn. From 1986 to 2023 he taught Mathematics at the Technical University of Berlin. From 1995 to 1996 he was Five College Professor in Amherst. From 1992 to 2002 he was head of the Sonderforschungsbereich Differential Geometry and Quantum Physics.

Oliver Gross received his [...]. and [...]. in Mathematics at TU Berlin in 2019 and 2020 respectively. Currently he is a researcher in the collaborative research center SFB TRR 109 "Discretization in Geometry and Dynamics" at TU Berlin under the supervision of Prof. Ulrich Pinkall.

Zusammenfassung

This book is open access, which means that you have free and unlimited access.

Focusses on variational problems

Includes a large number of graphical illustrations

Presents historic backgrounds and notes

Inhaltsverzeichnis
- Part I Curves. - 1. Curves in Rn. - 2. Variations of Curves. - 3. Curves in R2. - 4. Parallel Normal Fields. - 5. Curves in R3. - Part II Surfaces. - 6. Surfaces and Riemannian Geometry. - 7. Integration and Stokes' Theorem. - 8. Curvature. - 9. Levi-Civita Connection. - 10. Total Gaussian Curvature. - 11. Closed Surfaces. - 12. Variations of Surfaces . - 13. Willmore Surfaces.
Details
Erscheinungsjahr: 2024
Fachbereich: Geometrie
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Compact Textbooks in Mathematics
Inhalt: xi
203 S.
14 s/w Illustr.
66 farbige Illustr.
203 p. 80 illus.
66 illus. in color.
ISBN-13: 9783031398377
ISBN-10: 3031398378
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Gross, Oliver
Pinkall, Ulrich
Hersteller: Springer Nature Switzerland
Springer International Publishing
Springer International Publishing AG
Compact Textbooks in Mathematics
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 235 x 155 x 12 mm
Von/Mit: Oliver Gross (u. a.)
Erscheinungsdatum: 14.02.2024
Gewicht: 0,375 kg
Artikel-ID: 127200625
Über den Autor
Ulrich Pinkall was born in 1955. In 1979 he graduated in Mathematics and Physics at the University of Freiburg, where in 1981 he also got his PhD in Mathematics. From 1984 to 1986 he worked at the MPI für Mathematik in Bonn. From 1986 to 2023 he taught Mathematics at the Technical University of Berlin. From 1995 to 1996 he was Five College Professor in Amherst. From 1992 to 2002 he was head of the Sonderforschungsbereich Differential Geometry and Quantum Physics.

Oliver Gross received his [...]. and [...]. in Mathematics at TU Berlin in 2019 and 2020 respectively. Currently he is a researcher in the collaborative research center SFB TRR 109 "Discretization in Geometry and Dynamics" at TU Berlin under the supervision of Prof. Ulrich Pinkall.

Zusammenfassung

This book is open access, which means that you have free and unlimited access.

Focusses on variational problems

Includes a large number of graphical illustrations

Presents historic backgrounds and notes

Inhaltsverzeichnis
- Part I Curves. - 1. Curves in Rn. - 2. Variations of Curves. - 3. Curves in R2. - 4. Parallel Normal Fields. - 5. Curves in R3. - Part II Surfaces. - 6. Surfaces and Riemannian Geometry. - 7. Integration and Stokes' Theorem. - 8. Curvature. - 9. Levi-Civita Connection. - 10. Total Gaussian Curvature. - 11. Closed Surfaces. - 12. Variations of Surfaces . - 13. Willmore Surfaces.
Details
Erscheinungsjahr: 2024
Fachbereich: Geometrie
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Compact Textbooks in Mathematics
Inhalt: xi
203 S.
14 s/w Illustr.
66 farbige Illustr.
203 p. 80 illus.
66 illus. in color.
ISBN-13: 9783031398377
ISBN-10: 3031398378
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Gross, Oliver
Pinkall, Ulrich
Hersteller: Springer Nature Switzerland
Springer International Publishing
Springer International Publishing AG
Compact Textbooks in Mathematics
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 235 x 155 x 12 mm
Von/Mit: Oliver Gross (u. a.)
Erscheinungsdatum: 14.02.2024
Gewicht: 0,375 kg
Artikel-ID: 127200625
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