Glossary of Riemannian and metric geometry information

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...

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...

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

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...

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...

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...

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,...

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

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

In theoretical physics, quantum geometry is the set of mathematical concepts generalizing the concepts of geometry whose understanding is necessary to...

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

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

the tangent bundle TM of a manifold, and the metric on E is induced by a Riemannian metric on M. Another special case of a metric connection is a Yang–Mills...

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:...

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

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

consider more complicated fields. For example, if the manifold is Riemannian, then it has a metric field g {\displaystyle g} , such that given any two vectors...