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# Topic: Glossary of differential geometry and topology

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 Differential geometry and topology - Wikipedia, the free encyclopedia Differential geometry is the study of geometry using differential calculus (cf. Initially and up to the middle of the nineteenth century, differential geometry was studied from the extrinsic point of view: curves and surfaces were considered as lying in a Euclidean space of higher dimension (for example a surface in an ambient space of three dimensions). A vector field is a function from a manifold to the disjoint union of its tangent spaces (this union is itself a manifold known as the tangent bundle), such that at each point, the value is an element of the tangent space at that point. en.wikipedia.org /wiki/Differential_geometry   (1706 words)

 Glossary of differential geometry and topology - Wikipedia, the free encyclopedia This is a glossary of terms specific to differential geometry and differential topology. Given two differentiable manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both or smooth manifold is a differentiable manifold whose chart overlap functions are infinitely continuously differentiable. en.wikipedia.org /wiki/Submanifold   (497 words)

 Differential geometry and topology Article, Differentialgeometryandtopology Information   (Site not responding. Last check: 2007-10-23) In mathematics, differential topology is the fielddealing with differentiable functions on differentiable manifolds. Initially and up to the middle of the nineteenth century,differential geometry was studied from the extrinsic point of view: curves, surfaces were considered as lying in a Euclidean space of higher dimension (for example a surface in an ambient space of three dimensions). The apparatus of differential geometry is that of calculus on manifolds: this includes the study of manifolds, tangent bundles, cotangent bundles, differential forms, exterior derivatives, integrals of p-forms over p-dimensional submanifolds and Stokes' theorem, wedgeproducts, and Lie derivatives. www.anoca.org /space/manifold/differential_geometry_and_topology.html   (920 words)

 The Ultimate Differential geometry and topology Dog Breeds Information Guide and Reference The apparatus of differential geometry is that of calculus on manifolds: this includes the study of manifolds, tangent bundles, cotangent bundles, differential forms, exterior derivatives,integrals of p-forms over p-dimensional submanifolds and Stokes' theorem, wedge products, and Lie derivatives. We say a function from the manifold to R is infinitely differentiable if its composition with every homeomorphism results in an infinitely differentiable function from the open unit ball to R. This is an analog of symplectic geometry which works for manifolds of odd dimension. www.dogluvers.com /dog_breeds/Differential_geometry   (990 words)

 [No title] Topology Glossary Mainly extracted from (a) UC Davis Math:Profile Glossary (http://www.math.ucdavis.edu/profiles/glossary.html) by Greg Kuperberg (http://www.math.ucdavis.edu/profiles/kuperberg.html), and (b) Topology Atlas Glossary (http://www.achilles.net/~mtalbot/TopoGloss.html). differential geometry The general study of smooth manifolds decorated by continuous structures such as foliations, Riemannian metrics, and symplectic structures. An early result in topology states that every closed 3-manifold (closed meaning that the manifold is finite and connected but has no boundary) has a Heegaard splitting and a resulting description in terms of a Heegaard diagram, which describes how the two handlebodies are glued together. www.ornl.gov /sci/ortep/topology/defs.txt   (5717 words)

 Glossary of differential geometry and topology - Encyclopedia, History, Geography and Biography Glossary of differential geometry and topology - Encyclopedia, History, Geography and Biography Given two differentiable manifolds M and N, a bijective map $f$ from M to N is called a diffeomorphism if both $f:M\to N$ and its inverse $f^\left\{-1\right\}:N\to M$ are smooth functions. Glossary of differential geometry and topology, A, B, C, D, E, F, G, H, I, L, M, P, S, T, V, W, Differential geometry, Differential topology and Glossaries. www.arikah.net /encyclopedia/Submanifold   (553 words)

 Encyclopedia :: encyclopedia : Differential geometry   (Site not responding. Last check: 2007-10-23) In mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties that are invariant under the projective group. Élie Cartan formulated the idea of a general projective connection, as part of his method of moving frames; abstractly speaking, this is the level of generality at which the Erlangen program can be reconciled with differential geometry, while it also develops the oldest part of the theory (for the projective line), namely the Schwarzian derivative. The ideas of projective differential geometry recur in mathematics and its applications, but the formulations given are still rooted in the language of the early twentieth century. www.hallencyclopedia.com /Differential_geometry   (332 words)

 Geometry of Surfaces - From Monitor-Data.com Store This text intends to provide the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. Stillwell contends (in his preface) that the geometry of surfaces of constant curvature is an ideal topic for such a course, and he gives three convincing reasons for that, the most important one being "maximal connectivity with the rest of mathematics," which he elucidates. It is an attractive mixture of topology, algebra and a smidgen of analysis. www.monitor-data.com /books/0387977430.html   (798 words)

 UC Davis Math: Glossary The study of the geometry in the complex plane of complex analytic functions, in particular the relation between the image of the unit disk of an analytic function and its power series. The partial differential equation u_t + uu_x + u_xxx = 0 which is important both in applied mathematics, because of the physical phenomena it models, and in pure mathematics, because of the structure of its solutions. In topology, the terms circle and sphere refer to topological objects and not geometric ones, so that the surface of an egg shape is a sphere. www.math.ucdavis.edu /glossary.html   (9932 words)

 Wikinfo | Differential geometry and topology Riemannian geometry has Riemannian manifold as the main object of study, its smooth manifolds with an additional structure which makes them look infinitesimally like Euclidean space and therefore allow to generalise the notion from Euclidean geometry such as gradient of a function, divergence, length of curves and so on. Images, some of which are used under the doctrine of Fair use or used with permission, may not be available. www.internet-encyclopedia.org /wiki.php?title=Differential_geometry   (906 words)

 Geometry - Gurupedia Geometry is the branch of mathematics dealing with spatial relationships. analytic geometry, in which coordinate systems are introduced and points are represented as ordered pairs or triples of numbers. The central notion in geometry is that of congruence. www.gurupedia.com /g/ge/geometry.htm   (294 words)

 Differential geometry - ExampleProblems.com A differential manifold is a topological space with a collection of homeomorphisms from open sets of the space to open subsets in R Smooth manifolds are 'softer' than manifolds with extra geometric stuctures, which can act as obstructions to certain types of equivalences and deformations that exist in differential topology. Unlike in Riemannian geometry, all symplectic manifolds are locally isomorphic, so the only invariants of a symplectic manifold are global in nature. www.exampleproblems.com /wiki/index.php/Differential_geometry   (1307 words)

 Open Questions: Mathematics Point set topology was an abstraction from geometry which retained almost nothing except for the notion of what it meant for points to be "near" each other. Differentiable manifolds have at each point what is known as a "tangent space", which is quite analogous to the tangent line to a smooth curve. "Differential topology" and "differential geometry" are often referred to as subfields of modern geometry (and/or topology). www.openquestions.com /oq-math.htm   (8934 words)

 List of mathematics lists - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-10-23) Geometry is initially the study of spatial figures like circles and cubes, though it has been generalized considerably. Topology developed from geometry; it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems. tramadol.tfres.net /wiki/List_of_mathematics_lists   (963 words)

 Web Glossary -- Recommendations and Resources   (Site not responding. Last check: 2007-10-23) This is a glossary of some terms used in the branch of mathematics known as topology. It seems that the current glossary is evolving into a "general topology" glossary (i.e. The word ''glossary'' itself is derived from the Greek ''glossa'' (γλωσσα) meaning "tongue". www.becomingapediatrician.com /health/167/web-glossary.html   (906 words)

 Brujula.Net - Your Latin Stating Point   (Site not responding. Last check: 2007-10-23) Geometry deals with spatial relationships, using fundamental qualities or axioms. See also Glossary of differential geometry and topology, Main article. differential topology, which looks at the properties of differentiable functions defined over a manifold. www.brujula.net /english/wiki/Areas_of_mathematics.html   (563 words)

 List of glossaries - Wikipedia, the free encyclopedia This is a list of glossaries (pages containing terms and their definitions or explanations). Jabberwocky glossary words from the poem from Through the Looking-Glass, and What Alice Found There by Lewis Carroll Glossary of medical terms related to communications disorders en.wikipedia.org /wiki/List_of_glossaries   (138 words)

 Glossary of differential geometry and topology - Gurupedia Glossary of differential geometry and topology - Gurupedia This is a glossary of terms specific to Given two differentiable manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both and its inverse are smooth. www.gurupedia.com /c/co/codimension.htm   (465 words)

 Open Questions: Geometry and Topology This was a "top down" or "wholistic" view of geometry, in that it did not seek to analyze geometric objects in terms of their constituent parts (such as points or lines). Differential equations of mathematical physics, such as Maxwell's equations, are efficiently expressed in a coordinate-independent way using the language of manifold theory. The maps establishing equivalence between differentiable manifolds are called diffeomorphisms, and the category is known as the category of differentiable manifolds, or alternatively, smooth manifolds. www.openquestions.com /oq-ma003.htm   (14549 words)

 Math, Science   (Site not responding. Last check: 2007-10-23) Algebraic Topology Discussion List - The primary functions of this list are: providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, and serving as a forum for topics related to algebraic topology. Topology - Descriptions and illustrations of several topological and differential geometry related notions. Topology of Manifolds: Supersymmetry and QFT - This is the web resource page for a course taught by John Morgan in Fall 1997 at Columbia University. www.sorf.net /ara/en/scat.asp?ID=Science/Math/Topology   (477 words)

 Awesome Library - Mathematics Provides basic geometry tutorials by topic, incuding parallel lines, triangles (congruent, right, isosceles, and equilateral), quadrilaterals, parallelograms, ratios, polygons, circles, squares, rhombuses, trapezoids, volumes, areas, pyramids, cylinders, cones, spheres, prisms, arcs, angles, chords, radius or radii, Pythagorean theorem, intersections, slopes, tangents, secants, circumferences, coordinate geometry, and more. Provides carefully selected sources of lessons in fractions and decimals, geometry and measurement, patterns and relationships, and whole number operations. The geometry of Euclid was known for many centuries as 'the' geometry, but is nowadays referred to as Euclidean geometry." 8-05 www.awesomelibrary.org /Classroom/Mathematics/Middle-High_School_Math/Geometry.html   (1036 words)

 MATHEMATICS Differential and integral calculus, with examples from the life sciences. MATH 444 Geometry for Teachers (3) NW Concepts of geometry from multiple approaches; discovery, formal and informal reasoning, transformations, coordinates, exploration using computers and models. MATH 445 Geometry for Teachers (3) NW Concepts of geometry from multiple approaches; discovery, formal and informal reasoning, transformations, coordinates, exploration using computers and models. www.washington.edu /students/crscat/math.html   (5110 words)

 Glossary of terms for Fermat's Last Theorem It is a way to define "partial differentiation" of a function on a manifold in a manner that takes account of the geometry of the manifold. Examples include differential equations, the periodicity property f(z+t) = f(t), the symmetry property of an automorphic function, and relationships between function values at different points such as the functional equations of the Riemann zeta function and L-functions. The points of the quotient space are equivalence classes, and the topology is the strongest one such that the projection map is continuous. cgd.best.vwh.net /home/flt/flt10.htm   (2633 words)

 math lessons - Hypersurface For differential geometry usage, see glossary of differential geometry and topology. In algebraic geometry, a hypersurface in projective space of dimension n is an algebraic set that is purely of dimension n − 1. algebra arithmetic calculus equations geometry differential equations trigonometry number theory probability theory applied mathematics mathematical games mathematicians www.mathdaily.com /lessons/Hypersurface   (102 words)

 Geometry & Topology - Books - Magic Bean Dip The problem with Americas schools are that Geometry Teachers dont teach the subject the right way either by not teaching the material or they teach the students to maximize their test score by regurgitating concepts. One major gripe is that I wish on the solid geometry section, they would put problems involving the areas of a decagonal prism, dodecagonal prism, 20 sided pyramids. I wish this was the standard of geometry books because Americas students need to be challenged, a lot of students want to be challenged. v1.magicbeandip.com /store/browse_books_226700   (1742 words)

 Convex Integration Theory   (Site not responding. Last check: 2007-10-23) Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. The book should prove useful to graduate students and to researchers in topology, PDE theory and optimal control theory who wish to understand the h-principle and how it can be applied to solve problems in their respective disciplines. www.booksmatter.com /b376435805x.htm   (240 words)

 [No title]   (Site not responding. Last check: 2007-10-23) This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. A caveat: many terms in Riemannian and metric geometry, such as convex function, convex set and others, do not have exactly the same meaning as in general mathematical usage. Word metric on a group is a metric of the Cayley graph constructed using a set of generators. www.brujula.net /english/wiki/Glossary_of_Riemannian_and_metric_geometry.html   (1131 words)

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