Differential Geometry by Ulrich Pinkall, Oliver Gross
Differential Geometry: From Elastic Curves to Willmore Surfaces - Table of Contents
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
A. Some Technicalities
B. Timeline
What You Will Learn in Differential Geometry: From Elastic Curves to Willmore Surfaces
"Differential Geometry: From Elastic Curves to Willmore Surfaces" by "Ulrich Pinkall" and "Oliver Gross" is a clear and concise introduction to "differential geometry", designed for students and researchers in mathematics, physics, and applied fields. The book provides a solid foundation in the study of curves, surfaces, and manifolds, bridging rigorous "mathematical theory" with intuitive geometric understanding. It emphasizes essential concepts such as tangent spaces, "curvature", geodesics, and vector fields, making complex ideas accessible to readers with a background in advanced mathematics.
The text is structured to gradually build understanding, starting with basic definitions and examples before moving into more advanced topics in "Riemannian geometry" and manifold theory. Pinkall and Gross include numerous illustrations, computations, and exercises to reinforce learning and connect abstract concepts to practical applications. Readers are guided through the geometry of surfaces and curves, with careful explanations of curvature, torsion, and metric properties, highlighting the connections between local and global geometric behavior.
Beyond theory, the book demonstrates applications of differential geometry in physics, computer graphics, and geometric modeling. Its emphasis on "geometric analysis" and structured explanations helps readers develop both conceptual and computational skills. Serving as both a course textbook and a reference, "Differential Geometry" by Pinkall and Gross is an essential resource for understanding modern "geometry" and its applications in science and engineering.
Book Details & Specifications
Title:
Differential Geometry by Ulrich Pinkall, Oliver Gross
Publisher:
Birkhäuser
Year:
2014
Pages:
204
Type:
PDF
Language:
English
ISBN-10 #:
3031398378
ISBN-13 #:
978-3031398377
License:
CC BY-NC-ND 4.0
Amazon:
Amazon
About the Author: Ulrich Pinkall and Oliver Gross
The author
Ulrich Pinkall and Oliver Gross
are renowned "mathematicians" specializing in "differential geometry", "Riemannian geometry", and "geometric analysis". They focus on the study of curves, surfaces, and manifolds, combining rigorous "mathematical theory" with clear explanations and practical applications. Pinkall is known for his work in surface geometry and geometric modeling, while Gross emphasizes teaching and research in differential geometry. Together, they authored *Differential Geometry* to provide a structured, accessible guide for students and researchers. Their book bridges theory and applications, making advanced "geometry" concepts understandable for mathematics, physics, and computational modeling.
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