Ambient space

An ambient space, or ambient configuration space and electroambient space, is the space surrounding an object.

[edit] Mathematics

Three examples of different geometries: Euclidean, elliptical and hyperbolic geometry.

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

• Maxwell equations
• Manifold and ambient manifold
• Submanifolds and Hypersurfaces
• Riemannian manifolds
• Ricci curvature
• Radiant energy
• FDTD and GMRES
• Poisson equation
• Green's function (many-body theory)
• Krylov subspace
• electric field
• inductor and capacitor
• Supernodes
• eigenvalues
• M-matrix
• continuity equation
• finite element method
• differential form
• vector potential and vector field

[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 particluar attention to page 120+.)
• Stephen Wiggins , Chaotic Transport in Dynamical Systems. 1992. (ed., with particluar 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