Lie Sphere Geometry : With Applications to Submanifolds
- Author
- Thomas E. Cecil
- Publication Year
- 2008
- Publisher
- Springer
- Language
- English
- Document Type
- Book
- Faculty / Subject Heading
- Mathematics and Statistics
- Download Book Read book
Provides a clear and comprehensive modern treatment of Lie sphere geometry and its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. The link with Euclidean submanifold theory is established via the Legendre map, which provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres.
Keywords: Mathematics and Statistics / Dimension / Grad / Curvature / Differential geometry / Manifold / Projective geometry
