infinitesimal neighborhood
1Beauville–Laszlo theorem — In mathematics, the Beauville–Laszlo theorem is a result in commutative algebra and algebraic geometry that allows one to glue two sheaves over an infinitesimal neighborhood of a point on an algebraic curve. It was proved by Harvard… …
2Charts on SO(3) — In mathematics, the special orthogonal group in three dimensions, otherwise known as the rotation group SO(3), is a naturally occurring example of a manifold. The various charts on SO(3) set up rival coordinate systems: in this case there cannot… …
3Grothendieck connection — In algebraic geometry and synthetic differential geometry, a Grothendieck connection is a way of viewing connections in terms of descent data from infinitesimal neighbourhoods of the diagonal.Introduction and motivationThe Grothendieck connection …
4Jacobi field — In Riemannian geometry, a Jacobi field is a vector field along a geodesic gamma in a Riemannian manifold describing the difference between the geodesic and an infinitesimally close geodesic. In other words, the Jacobi fields along a geodesic form …
5Projective connection — In differential geometry, a projective connection is a type of Cartan connection on a differentiable manifold. The structure of a projective connection is modeled on the geometry of projective space, rather than the affine space corresponding to… …
6Continuous function — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …
7Lie group — Lie groups …
8Connection (mathematics) — In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. There are a variety of kinds of connections in modern geometry, depending on what sort of… …
9Rotation matrix — In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix rotates points in the xy Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian… …
10Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …
