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 and Curvature Forms
- 9. Levi-Civita Connection
- 10. Total Gaussian Curvature
- 11. Closed Surfaces
- 12. Variations of Surfaces
- 13. Willmore Surfaces
- A. Technical Details
- B. Timeline
What You Will Learn in Differential Geometry: From Elastic Curves to Willmore Surfaces
Differential Geometry by Ulrich Pinkall and Oliver Gross presents a structured, modern treatment of intrinsic and extrinsic geometry. Studying this high-level differential geometry textbook pdf introduces students and researchers to smooth manifolds, tangent bundles, vector fields, and exterior differential calculus.
The text thoroughly examines curves and surfaces in Euclidean space, Riemannian metrics, Levi-Civita connections, geodesics, and the Gauss-Bonnet theorem. Utilizing this resource as a differential geometry book pdf free download provides clear geometric intuition alongside precise analytical proofs necessary for advanced study in modern analysis and theoretical physics.
As a valuable addition to our collection of differential geometry books free download, this guide serves as an ideal reference for graduate students, geometers, and mathematical physicists aiming to master differential forms and curvature dynamics.
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
The author Ulrich Pinkall
is a distinguished German mathematician and Professor of Differential Geometry and Mathematical Visualization at the Technical University of Berlin (TU Berlin), recognized globally for his groundbreaking contributions to discrete differential geometry and mathematical graphics.
Together with co-author Christian Gross, their collaborative work Differential Geometry by Pinkall and Gross synthesizes decades of pedagogical clarity and cutting-edge geometric research into a clear, student-friendly resource.
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