This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following...

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an...

Complete metric space – Metric geometry Diversity (mathematics) – Generalization of metric spaces Glossary of Riemannian and metric geometry – Mathematics...

general topology Glossary of algebraic topology Glossary of Riemannian and metric geometry. See also: List of differential geometry topics Words in italics...

This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory...

defines some notion of size, distance, shape, volume, or other rigidifying structure. For example, in Riemannian geometry distances and angles are specified...

or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs...

aspherical. This fact is of crucial importance for modern geometric group theory. Glossary of Riemannian and metric geometry Cartan–Hadamard manifold...

stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries without the...

In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface)...

and bending, like dimension. Glossary of differential geometry and topology Glossary of general topology Glossary of Riemannian and metric geometry Glossary...

of Riemannian metrics which measures the failure of the second covariant derivatives to commute. A Riemannian manifold has zero curvature if and only...

the study of Riemannian geometry and more generally metric geometry. In general relativity, geodesics in spacetime describe the motion of point particles...

differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces...

point. This can be studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through Lie theory...

Glossary of differential geometry and topology Glossary of areas of mathematics Glossary of Riemannian and metric geometry Vickers (1989) p.22 Hart,...

This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. List of curves topics...

important class of manifolds are differentiable manifolds; their differentiable structure allows calculus to be done. A Riemannian metric on a manifold...

commutative algebra Glossary of differential geometry and topology Glossary of invariant theory Glossary of Riemannian and metric geometry Glossary of scheme theory...

metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures all the geometric and causal...

In Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine...

tensor of the Newtonian potential. Bernhard Riemann Curvature Glossary of Riemannian and metric geometry Ohanian, Hans (1976). Gravitation and Spacetime...

whatever matter and radiation are present. A version of non-Euclidean geometry, called Riemannian geometry, enabled Einstein to develop general relativity...

choice of Riemannian metric and are only invariant up to isometry. Bloch, Ethan D. (1996). A First Course in Geometric Topology and Differential Geometry. Boston:...

universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe...

called geodesics. The Riemannian geometry used in general relativity is an example of such a geometry. In spherical geometry, length is measured along...

2022-10-04. McInerney, Andrew (2013-07-09). First Steps in Differential Geometry: Riemannian, Contact, Symplectic. Springer Science & Business Media. pp. 136–155...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

Noncommutative geometry Ashtekar, Abhay; Corichi, Alejandro; Zapata, José A. (1998), "Quantum theory of geometry. III. Non-commutativity of Riemannian structures"...

conformal class of metrics is equivalent to a unique complex one, and 4-dimensional topology can be studied from the point of view of complex geometry in two variables...