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A geometry in which Archimedes' axiom does not hold.

Three point geometry is a finite geometry subject to the following four axioms: 1. There exist exactly three points. 2. Two distinct points are on exactly one line. 3. Not ...

Five point geometry is a finite geometry subject to the following three axioms: 1. there exist exactly five points, 2. each two distinct points have exactly one line on both ...

Classical algebraic geometry is the study of algebraic varieties, both affine varieties in C^n and projective algebraic varieties in CP^n. The original motivation was to ...

Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional ...

In the algebraic geometry of Grothendieck, a stack refers to a sheaf of categories. In particular, a stack is a presheaf of categories in which the following descent ...

The frame bundle on a Riemannian manifold M is a principal bundle. Over every point p in M, the Riemannian metric determines the set of orthonormal frames, i.e., the possible ...

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 ...

Any collineation from P(V) to P(V), where V is a three-dimensional vector space, is associated with a semilinear map from V to V.

A geodesic mapping f:M->N between two Riemannian manifolds is a diffeomorphism sending geodesics of M into geodesics of N, whose inverse also sends geodesics to geodesics ...