Ambient space (mathematics)
An ambient space or ambient configuration space is the space surrounding an object.
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.
See also
- Configuration space
- Manifold and ambient manifold
- Submanifolds and Hypersurfaces
- Riemannian manifolds
- Ricci curvature
- Differential form
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