08-12-2026, 10:01 AM
Differential Geometry
ΒΥ Ulrich Pinkall , Oliver Gross
Summary
Differential Geometry: From Elastic Curves to Willmore Surfaces by Ulrich Pinkall and Oliver Gross is an open-access textbook that provides an accessible introduction to the differential geometry of curves and surfaces, with particular emphasis on variational problems—understanding shapes that minimize physically meaningful quantities such as length, area, or bending energy.
The book develops the theory from curves in $\mathbb{R}^n$, $\mathbb{R}^2$, and $\mathbb{R}^3$ to surfaces and Riemannian geometry, covering curvature, the Levi-Civita connection, Stokes' theorem, Gaussian curvature, the Gauss–Bonnet theorem, minimal surfaces, and Willmore surfaces. A distinctive feature is its strong use of geometric illustrations and physical interpretations, making the material relevant not only to pure mathematics but also to physics, engineering, and computer graphics, while providing a foundation for further study of manifolds.
EBOOK
ΒΥ Ulrich Pinkall , Oliver Gross
Quote:This book is provided as open access and is
available for download [12/08/2026]
Summary
Differential Geometry: From Elastic Curves to Willmore Surfaces by Ulrich Pinkall and Oliver Gross is an open-access textbook that provides an accessible introduction to the differential geometry of curves and surfaces, with particular emphasis on variational problems—understanding shapes that minimize physically meaningful quantities such as length, area, or bending energy.
The book develops the theory from curves in $\mathbb{R}^n$, $\mathbb{R}^2$, and $\mathbb{R}^3$ to surfaces and Riemannian geometry, covering curvature, the Levi-Civita connection, Stokes' theorem, Gaussian curvature, the Gauss–Bonnet theorem, minimal surfaces, and Willmore surfaces. A distinctive feature is its strong use of geometric illustrations and physical interpretations, making the material relevant not only to pure mathematics but also to physics, engineering, and computer graphics, while providing a foundation for further study of manifolds.
EBOOK
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