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A set in R^d formed by translating an affine subspace or by the intersection of a set of hyperplanes.

In elliptic n-space, the pole of an (n-1)-flat is a point located at an arc length of pi/2 radians away from each point of the (n-1)-flat.

The flat norm on a current is defined by F(S)=int{Area T+Vol(R):S-T=partialR}, where partialR is the boundary of R.

A module M over a unit ring R is called flat iff the tensor product functor - tensor _RM (or, equivalently, the tensor product functor M tensor _R-) is an exact functor. For ...

A manifold with a Riemannian metric that has zero curvature is a flat manifold. The basic example is Euclidean space with the usual metric ds^2=sum_(i)dx_i^2. In fact, any ...

A module M over a unit ring R is called faithfully flat if the tensor product functor - tensor _RM is exact and faithful. A faithfully flat module is always flat and ...

If it is possible to transform a coordinate system to a form where the metric elements g_(munu) are constants independent of x^mu, then the space is flat.

A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

A connection game is a board game in which players compete to develop or complete a type of topological connection with their pieces. This could involve forming a path ...

On a Riemannian manifold M, there is a canonical connection called the Levi-Civita connection (pronounced lē-vē shi-vit-e), sometimes also known as the Riemannian connection ...