Differential Geometry

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.
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

Autor*in

Ulrich Pinkall

Themen in »Differential Geometry«

Open Access Surfaces Curves Elastic Minimal Willmore Variational Calculus Riemannian Geometry

Stimmen zu »Differential Geometry«

“One remarkable feature of the book is the attempt of the authors to develop the theory of the curves and the surfaces in a parallel way. ... The book is very visual in the sense that the authors don’t shy away from referring to pictures whenever it is in the interest of the readers ... . Concerning the pictures, which are very colorful and high quality ... . The mechanical and physical associations and interpretations are used throughout the book.” (Yagub Aliyev, zbMATH 1579.53002, 2026)

Details

Link teilen