Ambient space
From Wikipedia, the free encyclopedia
An ambient space, ambient configuration space, or electroambient space, is the space surrounding an object.
[edit] Mathematics
In mathematics, especially in geometry and topology, an ambient space is the space surrounding a mathematical object. For example, a line may be studied in isolation, or it may be studied as an object in two-dimensional space — in which case the ambient space is the plane, or as an object in three-dimensional space — in which case the ambient space is three-dimensional. To see why this makes a difference, consider the statement "Lines that never meet are necessarily parallel." This is true if the ambient space is two-dimensional, but false if the ambient space is three-dimensional, because in the latter case the lines could be skew lines, rather than parallel.
[edit] See also
- Configuration space
- Manifold and ambient manifold
- Submanifolds and Hypersurfaces
- Riemannian manifolds
- Ricci curvature
- differential form
[edit] Further reading
- W H A Schilders, E.J .W. ter Maten, Philippe G. Ciarlet, Numerical Methods in Electromagnetics: Special Volume, Elsevier 2005. (ed., with particular attention to page 120+.)
- Stephen Wiggins , Chaotic Transport in Dynamical Systems. 1992. (ed., with particular attention to page 209+.)
- "Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps" arXiv:0708.3578, 2007
- "Relative Hyperbolic Extensions of Groups and Cannon-Thurston Maps" arXiv:0801.0933, 2008
