ones. Roughly speaking, the pullback mechanism (using precomposition) turns several constructions in differential geometry into contravariant functors...

Pullbacks can be applied to many other objects such as differential forms and their cohomology classes; see Pullback (differential geometry) Pullback...

field Tensor field Differential form Exterior derivative Lie derivative pullback (differential geometry) pushforward (differential) jet (mathematics)...

This is a glossary of terms specific to differential geometry and differential topology. The following three glossaries are closely related: Glossary of...

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most...

under pullback. Differential forms are part of the field of differential geometry, influenced by linear algebra. Although the notion of a differential is...

In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common...

mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus...

In differential geometry, pushforward is a linear approximation of smooth maps (formulating manifold) on tangent spaces. Suppose that φ : M → N {\displaystyle...

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

mediating morphism u : Q → P above is not required to be unique. Pullbacks in differential geometry Equijoin in relational algebra Fiber product of schemes Mitchell...

construction is useful in differential geometry and topology. Bundles may also be described by their sheaves of sections. The pullback of bundles then corresponds...

transform composed as pullback onto the incidence graph and then push forward. Luis Santaló (1953) Introduction to Integral Geometry, Hermann (Paris) Wilhelm...

topology Pullback (differential geometry), a term in differential geometry Pullback (category theory), a term in category theory Pullback attractor, an aspect...

in conjunction with an origin) often used to study the extrinsic differential geometry of smooth manifolds embedded in a homogeneous space. In lay terms...

Diophantine geometry Glossary of classical algebraic geometry Glossary of differential geometry and topology Glossary of Riemannian and metric geometry List...

In differential geometry, the Lie derivative (/liː/ LEE), named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including...

2022-05-06. Kobayashi, Shoshichi; Nomizu, Katsumi (1969). Foundations of differential geometry. Vol II. Interscience Tracts in Pure and Applied Mathematics. Vol...

every point p ∈ N {\displaystyle \textstyle p\in N} is annihilated by (the pullback of) each ⁠ α i {\displaystyle \textstyle \alpha _{i}} ⁠. A maximal integral...

In differential geometry, a field in mathematics, Darboux's theorem is a theorem providing a normal form for special classes of differential 1-forms,...

In geometry, a valuation is a finitely additive function from a collection of subsets of a set X {\displaystyle X} to an abelian semigroup. For example...

[1993]. Differential manifolds. Mineola, New York: Dover Publications. ISBN 978-0-486-46244-8. Lang, Serge (1999). Fundamentals of Differential Geometry. Graduate...

vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a differential form with...

In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame...

a set equipped with a diffeology. Many of the standard tools of differential geometry extend to diffeological spaces, which beyond manifolds include arbitrary...

algebraic curves related these to intrinsic data, such as the regular differentials on a compact Riemann surface, and to extrinsic properties, such as embeddings...

which is formulated in the mathematics of differential geometry of differential manifolds. When this geometry is used as a model of spacetime, it is known...

differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator...

differential system ( M , I ) {\displaystyle (M,I)} consists of a submanifold N ⊂ M {\displaystyle N\subset M} having the property that the pullback to...

to other structures of differential geometry; the assimilation of the Kodaira–Spencer theory into the abstract algebraic geometry of Grothendieck, with...