Elementary Differential Geometry

• Main Author: Pressley, Andrew. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: London : Springer London, 2010.
• Edition: 2.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Global differential geometry.; Differential Geometry.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-84882-891-9

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions. It is a subject that contains some of the most bea...

Table of Contents:

• Curves in the plane and in space
• How much does a curve curve?
• Global properties of curves
• Surfaces in three dimensions
• Examples of surfaces
• The first fundamental form
• Curvature of surfaces
• Gaussian, mean and principal curvatures
• Geodesics
• Gauss<U+0019> theorema egregium
• Hyperbolic geometry
• Minimal surfaces
• The Gauss<U+0013>Bonnet theorem
• Inner product spaces and self-adjoint linear maps
• A1. Isometries of euclidean spaces
• A2. Mb̲ius transformations
• Hints to selected exercises
• Solutions.