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...

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

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

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...

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

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

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

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...

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

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

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

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

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

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...

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...

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

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

can also be viewed as a vector bundle morphism over X1 from E1 to the pullback bundle g*E2. Given a vector bundle π: E → X and an open subset U of X,...

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...

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

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 differential geometry, a field of mathematics, a normal bundle is a particular kind of vector bundle, complementary to the tangent bundle, and coming...

In the mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties...