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- ...geometric concepts of mathematics. For further background see [[history of manifolds and varieties]]. Manifolds in contemporary mathematics come in a number of types. These include: ...43 KB (5,826 words) - 13:16, 4 January 2025
- ...s there are various types of manifolds, there are various types of maps of manifolds. ...DIFF]], the category of [[piecewise]]-smooth maps between piecewise-smooth manifolds. ...5 KB (732 words) - 18:49, 29 January 2024
- ...>{{cite journal |doi=10.1021/i100012a019|title=Flow distribution in piping manifolds|journal=Industrial & Engineering Chemistry Fundamentals|volume=22|issue=4|p ...1>{{cite journal|last=Wang|first=J.Y.|title=Theory of flow distribution in manifolds|journal=Chemical Engineering J|year=2011|volume=168|issue=3|pages=1331–1345 ...13 KB (2,046 words) - 05:11, 17 January 2025
- ...astic calculus|stochastic analysis]] over [[Differentiable manifold|smooth manifolds]]. It is therefore a synthesis of stochastic analysis (the extension of [[c ...manifold|Riemannian metric]] to define martingales and Brownian motion on manifolds. Therefore, controlled by the Riemannian metric, Brownian motion will be a ...20 KB (3,336 words) - 01:21, 17 May 2024
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- ...nt union of manifolds. The ring is [[graded ring|graded]] by dimensions of manifolds and is denoted by where <math>\Omega^{SO}_n</math> consists of oriented cobordism classes of manifolds of dimension ''n''. One can also define an '''unoriented cobordism ring''', ...2 KB (283 words) - 17:39, 26 March 2024
- ...mov]].<ref>{{cite journal |last=Gromov |first=M. |title=Filling Riemannian manifolds |journal=J. Diff. Geom. |volume=18 |date=1983 |pages=1–147 |citeseerx=10.1. *All closed surfaces (i.e. 2-dimensional manifolds) are essential with the exception of the 2-sphere ''S<sup>2</sup>''. ...2 KB (290 words) - 20:09, 8 January 2025
- ...Ucci |first=John James |year=1965 |title=Immersions and embeddings of Dold manifolds |url=https://core.ac.uk/download/pdf/82435349.pdf |journal=[[Topology (jour [[Category:Manifolds]] ...1 KB (211 words) - 02:28, 7 May 2024
- ...cation in pure mathematics is Morse theory on manifolds with boundary, and manifolds with corners. ...rst=D. |last=Handron |title=Generalized billiard paths and Morse theory on manifolds with corners |journal=Topology and Its Applications |volume=126 |issue=1 |p ...2 KB (254 words) - 05:08, 29 January 2023
- ...) = x</math>.<ref name ="Lee_1988">{{citation|title=Introduction to Smooth Manifolds|volume=218|series=Graduate Texts in Mathematics|first=John|last=Lee|publish [[Category:Manifolds]] ...1 KB (152 words) - 01:51, 18 November 2024
- ...books.google.com/books?id=TASWAwAAQBAJ | title=The Geometric Topology of 3-manifolds | isbn=9780821810408 | last1=Bing | first1=R. H. | date=31 December 1983 }} ...1,003 bytes (144 words) - 22:36, 12 May 2024
- ...lzant polytope is the moment polytope of such a manifold, and any two such manifolds with equivalent moment polytopes (up to translations and <math>GL(n,\mathb ...2 KB (238 words) - 19:05, 30 September 2024
- ...] that cannot be expressed as a non-trivial [[connected sum]] of two ''n''-manifolds. Non-trivial means that neither of the two is an [[n-sphere|''n''-sphere]]. ...nected sum of a unique ([[up to]] [[homeomorphism]]) collection of prime 3-manifolds. ...7 KB (1,070 words) - 15:39, 22 June 2024
- ...=Blair|first1=David E.|title=Riemannian geometry of contact and symplectic manifolds|edition=Second edition of 2002 original|series=Progress in Mathematics|volu ...l|first1=Katsuei|last1=Kenmotsu|title=A class of almost contact Riemannian manifolds|journal=[[Tohoku Mathematical Journal]]|series=Second Series|volume=24|year ...2 KB (339 words) - 14:17, 4 October 2024
- * Shiing-Shen Chern, ''Complex Manifolds Without Potential Theory''. [[Category:Complex manifolds]] ...2 KB (265 words) - 16:27, 4 February 2025
- * {{Citation|last1=Tucker|first1=Thomas W.|title=Non-compact 3-manifolds and the missing-boundary problem|doi=10.1016/0040-9383(74)90019-6|year=1974 {{Manifolds}} ...2 KB (204 words) - 12:36, 18 August 2023
- ...first3=Shing Tung | title=The Poincaré–Lelong equation on complete Kähler manifolds | url=http://www.numdam.org/item?id=CM_1981__44_1-3_183_0 |mr=662462 | year [[Category:Complex manifolds]] ...1 KB (137 words) - 09:52, 10 September 2022
- ...is simply connected (in dimension 2, all simply connected compact complex manifolds are Kähler). Calabi and Eckmann discovered these manifolds in 1953.<ref>{{citation|first1=Eugenio|last1= Calabi|authorlink1=Eugenio Ca ...2 KB (368 words) - 13:04, 8 November 2023
- ...Binghamton]] with thesis ''Orbit maps of local <math>S^1</math>-actions on manifolds of dimension less than five '' under the supervision of Louis McAuley.<ref> His research deals with geometric topology, in particular of 4-manifolds (including the computation of Donaldson and Seiberg-Witten invariants) with ...6 KB (713 words) - 10:57, 7 April 2024
- ...ly, non Kählerian nearly Kähler manifolds are called "strict nearly Kähler manifolds". Nearly Kähler manifolds, also known as almost Tachibana manifolds, were studied by Shun-ichi Tachibana in 1959<ref> ...5 KB (821 words) - 03:50, 24 November 2023
- ...as. [[Graded manifold]]s are characterized by sheaves on [[manifold|smooth manifolds]], while [[supermanifold]]s are constructed by gluing of sheaves of [[super ...3 KB (385 words) - 22:35, 24 July 2022
- ...anifold. Broadly speaking, [[projective geometry]] refers to the study of manifolds with this kind of connection. ...manifolds with a conformal equivalence class of Riemannian metrics, i.e., manifolds modeled on the conformal sphere. Here the associated Cartan connection is ...3 KB (480 words) - 22:27, 10 January 2024
- ...[[geometric quantization]].</ref> suggest that the category of symplectic manifolds and symplectomorphisms be augmented by the inclusion of canonical relations ...1 KB (179 words) - 07:30, 6 April 2023
- ...s there are various types of manifolds, there are various types of maps of manifolds. ...DIFF]], the category of [[piecewise]]-smooth maps between piecewise-smooth manifolds. ...5 KB (732 words) - 18:49, 29 January 2024
- ...journal |author=Y. Nikolayevsky |year=2003 |title=Two theorems on Osserman manifolds |journal=Differential Geometry and Its Applications |volume=18 |issue=3 |pa ''Clifford structures'' are fundamental in studying Osserman manifolds. An [[Riemann curvature tensor|algebraic curvature tensor]] <math>R</math> ...5 KB (727 words) - 22:08, 5 February 2025