An ambient space or ambient configuration space is the space surrounding an object.
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.
- Configuration space
- Manifold and ambient manifold
- Submanifolds and Hypersurfaces
- Riemannian manifolds
- Ricci curvature
- differential form
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