Differential geometry

from elastic curves to Willmore surfaces

Ulrich Pinkall, Oliver Gross (Autoren)

Buch | Softcover

XI, 203 Seiten

2023 | 1. Auflage
Springer International Publishing (Verlag)
978-3-031-39837-7 (ISBN)

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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.

lt;b>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 B.Sc. and M.Sc. 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.

lt;b>Part I Curves.- Curves in Rn.- Variations of Curves.- Curves in R2.- Parallel Normal Fields. - Curves in R3.- Part II Surfaces.- Surfaces and Riemannian Geometry.- Integration and Stokes' Theorem.- Curvature.- Levi-Civita Connection.- Total Gaussian Curvature.- Closed Surfaces. - Variations of Surfaces.- Willmore Surfaces.

Erscheinungsdatum	15.02.2024
Reihe/Serie	Compact Textbooks in Mathematics
Zusatzinfo	Illustrationen
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	337 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Curves • Differential Geometry • elastic • Minimal • open access • Riemannian Geometry • Surfaces • variational calculus • Willmore
ISBN-10	3-031-39837-8 / 3031398378
ISBN-13	978-3-031-39837-7 / 9783031398377
Zustand	Neuware