Search for "Manifolds" in article titles:

1. Congruence (manifolds): In the theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold. Congruences are an important concept in general relativity, and are also important in parts of Riemannian ... (Manifolds) [100%] 2022-11-20 [Differential topology]
2. List of manifolds: Lie groups provide several interesting families. See Table of Lie groups for examples. (none) [81%] 2023-10-23 [Mathematics-related lists] [Manifolds]...
3. List of manifolds: This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics. (none) [81%] 2024-01-07 [Mathematics-related lists] [Manifolds]...
4. Topology of manifolds: The branch of the theory of manifolds (cf. Manifold) concerned with the study of relations between different types of manifolds. (Mathematics) [81%] 2024-01-26
5. Category of manifolds: In mathematics, the category of manifolds, often denoted Man, is the category whose objects are manifolds of smoothness class C and whose morphisms are p-times continuously differentiable maps. This is a category because the composition of two C maps ... (Category theory) [81%] 2024-01-07 [Categories in category theory] [Manifolds]...
6. Classification of manifolds: In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain. Formally, classifying manifolds is classifying objects up to isomorphism. [81%] 2024-01-08 [Differential geometry] [Manifolds]...
7. Maps of manifolds: In mathematics, more specifically in differential geometry and topology, various types of functions between manifolds are studied, both as objects in their own right and for the light they shed Just as there are various types of manifolds, there are ... [81%] 2023-09-13 [Maps of manifolds]
8. Integration on manifolds: Let $ M $ be a finite-dimensional smooth manifold. Tangent spaces and such provide the global analogues of differential calculus. (Mathematics) [81%] 2024-01-08
9. Structures on manifolds: There are three main types of structures important on manifolds. The foundational geometric structures are piecewise linear, mostly studied in geometric topology, and smooth manifold structures on a given topological manifold, which are the concern of differential topology as far ... [81%] 2023-10-18 [Abstract Algebra] [Manifolds]...
10. Topology of manifolds: The branch of the theory of manifolds (cf. Manifold) concerned with the study of relations between different types of manifolds. (Mathematics) [81%] 2023-10-18
11. Category of manifolds: In mathematics, the category of manifolds, often denoted Man, is the category whose objects are manifolds of smoothness class C and whose morphisms are p-times continuously differentiable maps. This is a category because the composition of two C maps ... [81%] 2024-01-07 [Manifolds]
12. Timeline of manifolds: This is a timeline of manifolds, one of the major geometric concepts of mathematics. For further background see history of manifolds and varieties. (Mathematics timeline) [81%] 2024-08-18 [Manifolds] [Mathematics timelines]...
13. Sphere theorem (3-manifolds): In mathematics, in the topology of 3-manifolds, the sphere theorem of Christos Papakyriakopoulos (1957) gives conditions for elements of the second homotopy group of a 3-manifold to be represented by embedded spheres. One example is the following: Let ... (3-manifolds) [70%] 2022-07-26 [Geometric topology] [3-manifolds]...
14. Introduction to 3-Manifolds: Introduction to 3-Manifolds is a mathematics book on low-dimensional topology. It was written by Jennifer Schultens and published by the American Mathematical Society in 2014 as volume 151 of their book series Graduate Studies in Mathematics. [70%] 2023-12-19 [Geometric topology] [Mathematics books]...
15. Differential geometry of manifolds: A branch of differential geometry dealing with various infinitesimal structures (cf. Infinitesimal structure) on a manifold and their connection with the structure of the manifold and its topology. (Mathematics) [70%] 2023-09-10
16. Geometry of immersed manifolds: A theory that deals with the extrinsic geometry and the relation between the extrinsic and intrinsic geometry (cf. also Interior geometry) of submanifolds in a Euclidean or Riemannian space. (Mathematics) [70%] 2023-09-06
17. Curvature of Riemannian manifolds: In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous way to define curvature ... [70%] 2023-10-22 [Curvature (mathematics)] [Differential geometry]...
18. Sphere theorem (3-manifolds): In mathematics, in the topology of 3-manifolds, the sphere theorem of Christos Papakyriakopoulos (1957) gives conditions for elements of the second homotopy group of a 3-manifold to be represented by embedded spheres. One example is the following: Let ... (3-manifolds) [70%] 2025-01-23 [Geometric topology] [3-manifolds]...
19. Introduction to 3-Manifolds: Introduction to 3-Manifolds is a mathematics book on low-dimensional topology. It was written by Jennifer Schultens and published by the American Mathematical Society in 2014 as volume 151 of their book series Graduate Studies in Mathematics. [70%] 2025-03-10 [Geometric topology] [Mathematics books]...
20. Prime decomposition of 3-manifolds: In mathematics, the prime decomposition theorem for 3-manifolds states that every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) finite collection of prime 3-manifolds. A manifold is prime if it cannot be ... [63%] 2022-11-11 [3-manifolds] [Manifolds]...
21. History of manifolds and varieties: The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave ... (Aspect of history of mathematics) [63%] 2024-05-17 [History of mathematics] [Manifolds]...
22. Prime decomposition of 3-manifolds: In mathematics, the prime decomposition theorem for 3-manifolds states that every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) finite collection of prime 3-manifolds. A manifold is prime if it cannot be ... [63%] 2025-02-03 [3-manifolds] [Manifolds]...
23. The geometry and topology of three-manifolds: The geometry and topology of three-manifolds is a set of widely circulated but unpublished notes by William Thurston from 1978 to 1980 describing his work on 3-manifolds. The notes introduced several new ideas into geometric topology, including orbifolds ... [53%] 2022-03-01 [Hyperbolic geometry] [3-manifolds]...