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...

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

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

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

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...

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)...

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

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

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...

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

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

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

classes of manifolds have canonical volume forms: they have extra structure which allows the choice of a preferred volume form. Oriented pseudo-Riemannian manifolds...

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...

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

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

theory Pseudo-Riemannian geometry generalizes Riemannian geometry to the study of pseudo-Riemannian manifolds. Pure mathematics the part of mathematics...

Zapata, José A. (1998), "Quantum theory of geometry. III. Non-commutativity of Riemannian structures", Classical and Quantum Gravity, 15 (10): 2955–2972,...

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

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

Ricci-Curbastro and Tullio Levi-Civita in the theory of Riemannian and pseudo-Riemannian geometry. Ricci and Levi-Civita (following ideas of Elwin Bruno Christoffel)...

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...

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:...

conservation of energy and momentum. The Einstein tensor G {\displaystyle {\boldsymbol {G}}} is a tensor of order 2 defined over pseudo-Riemannian manifolds...

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...

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

T ∗ M {\displaystyle \mathrm {T} ^{*}M} of a Riemannian or pseudo-Riemannian manifold induced by its metric tensor. There are similar isomorphisms on...