Surfaces in Classical Geometries A Treatment by Moving Frames /

• Main Authors: Jensen, Gary R. (Author), Musso, Emilio (Author), Nicolodi, Lorenzo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Universitext,
• Subjects: Mathematics.; Convex geometry.; Discrete geometry.; Differential geometry.; Differential Geometry.; Convex and Discrete Geometry.

Designed for intermediate graduate studies, this text will broaden students' core knowledge of differential geometry providing foundational material to relevant topics in classical differential geometry. The method of moving frames, a natural means for discovering and proving important results,...

Table of Contents:

• 1. Introduction
• 2. Lie Groups
• 3. Theory of Moving Frames
• 4. Euclidean Geometry
• 5. Spherical Geometry
• 6. Hyperbolic Geometry
• 7. Complex Structure
• 8. Minimal Immersions in Euclidean Space
• 9. Isothermic Immersions
• 10. The Bonnet Problem
• 11. CMC 1 Surfaces in H3
• 12. Möbius Geometry
• 13. Complex Structure and Möbius Geometry
• 14. Isothermic Immersions in Möbius Space
• 15. Lie Sphere Geometry
• Solutions to Select Problems
• References
• Index.