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Topic: Glossary of differential and metric geometry


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In the News (Mon 28 Dec 09)

  
  Differential geometry and topology - Biocrawler   (Site not responding. Last check: 2007-11-01)
Differential geometry is the study of geometry using calculus.
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).
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.
www.biocrawler.com /encyclopedia/Differential_geometry   (1066 words)

  
 NationMaster - Encyclopedia: Differential topology
Differential topology is the field of mathematics dealing with differentiable functions on differentiable manifolds.
A vector field is a function from a manifold to the disjoint union of its tangent spaces, such that at each point, the value is a member of the tangent space at that point.
A symplectic manifold is a differentiable manifold equipped with a closed non-degenerate bi-linear alternating form (a closed 2-form for short).
www.nationmaster.com /encyclopedia/Differential-topology   (1168 words)

  
 Spartanburg SC | GoUpstate.com | Spartanburg Herald-Journal   (Site not responding. Last check: 2007-11-01)
This distinction between differential geometry and differential topology is blurred, however, in questions specifically pertaining to local diffeomorphism invariants such as the tangent space at a point.
Differential topology is the study of the (infinitesimal, local, and global) properties of structures on manifolds having no non-trivial local moduli, whereas differential geometry is the study of the (infinitesimal, local, and global) properties of structures on manifolds having non-trivial local moduli.
CR geometry is the study of the intrinsic geometry of boundaries of domains in complex manifolds.
www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Differential_geometry   (2273 words)

  
 Differential geometry and topology Summary
Differential geometry is the study of geometry using differential calculus (cf.
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.
A symplectic manifold is a differentiable manifold equipped with a symplectic form (that is, a non-degenerate, bilinear, and skew-symmetric 2-form).
www.bookrags.com /Differential_geometry_and_topology   (2906 words)

  
  List of glossaries - Wikipedia, the free encyclopedia
Look up glossary in Wiktionary, the free dictionary.
This is a list of glossaries (pages containing terms and their definitions or explanations).
Glossary of medical terms related to communications disorders
en.wikipedia.org /wiki/List_of_glossaries   (135 words)

  
 Glossary of Riemannian and metric geometry - Definition, explanation
This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology.
Dilation of a map between metric spaces is the infimum of numbers L such that the given map is L-Lipschitz.
Word metric on a group is a metric of the Cayley graph constructed using a set of generators.
www.calsky.com /lexikon/en/txt/g/gl/glossary_of_riemannian_and_metric_geometry.php   (1188 words)

  
 Encyclopedia :: encyclopedia : Differential geometry   (Site not responding. Last check: 2007-11-01)
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)

  
 Reference.com/Encyclopedia/Riemannian geometry
In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics, i.e.
Riemannian geometry was first put forward in generality by Bernhard Riemann in the nineteenth century.
It deals with a broad range of geometries whose metric properties vary from point to point, as well as two standard types of Non-Euclidean geometry, spherical geometry and hyperbolic geometry, as well as Euclidean geometry itself.
www.reference.com /browse/wiki/Riemannian_geometry   (859 words)

  
 Glossary of differential geometry and topology - Definition, explanation
Glossary of differential geometry and topology - Definition, explanation
This is a glossary of terms specific to differential geometry and differential topology.
Tangent bundle, the vector bundle of tangent spaces on a differentiable manifold.
www.calsky.com /lexikon/en/txt/g/gl/glossary_of_differential_geometry_and_topology.php   (499 words)

  
 The Math Forum - Math Library - Geometry
A collection of handouts for a two-week summer workshop entitled 'Geometry and the Imagination', led by John Conway, Peter Doyle, Jane Gilman and Bill Thurston at the Geometry Center in Minneapolis, June 17-28, 1991.
Some notes on a most general definition of "geometry," first elucidated by Felix Klein, which is based on a set of geometric invariants under a group of transformations.
The FoCM's primary aim is to further the understanding of the deep relationships between mathematical analysis, topology, geometry and algebra and the computational process as they are evolving together with the modern computer.
mathforum.org /library/topics/geometry   (2310 words)

  
 Glossary — API Delevan   (Site not responding. Last check: 2007-11-01)
Differential Mode Noise: Noise signal measured between two points with respect to a common point less the common mode noise.
Field strength is determined by the magnitude of current and geometry of the windings.
MKS System: Meter-kilogram-second metric system of magnetic measurement, used for larger number calculations.
www.delevan.com /help_center/techlibrary/glossary.html   (4791 words)

  
 Metric Geometry
Metric geometry section of the mathematics e-print arXiv.
This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology.
Global and Local Metric Geometry of Ligand Binding Thermodynamics ED Cera and J Wyman
www.metricgeometry.info   (273 words)

  
 The Math Forum - Math Library - Calculus (SV)   (Site not responding. Last check: 2007-11-01)
Book I: functions and geometry; limits and continuity; the derivative; techniques and theory of differentiation; applications of the derivative; and integration.
Also includes a glossary of calculus terms and biographies, with definitions, theorems, and problems.
Sample problem solutions are linked to glossary terms and to procedural rules, and contents pages illustrate the linking of specific problems in a textbook to their solutions.
mathforum.org /library/topics/svcalc   (2601 words)

  
 Metric Measurement & Conversion - Mathematics, Weights Measurement, Metric Measurement Conversion,
Metric Prefixes - from yotta to yocto In introductory chemistry we use only a few of the most common metric prefixes, such as milli, centi, and kilo.
Metric units and Measurement Length Volume Mass Time Temperature Decimals in measurement Math Contests School League Competitions Contest Problem Books Challenging, fun math practice Educational Software Comprehensive Learning Tools Visit the Math League Length The standard unit of length in the metric system is the meter.
A note on the metric system: Before you use this table convert to the base measurement first, in that convert centi-meters to meters, convert kilo-grams to grams.
www.studysphere.com /Site/Sphere_773.html   (2081 words)

  
 Homework Hotline - Chemistry
From David Hsu, this shows the Periodic Table of the Elements, with a legend defining what type of element each one is. Each element leads to an in depth discussion of it's properties.
The references which are on this site include a glossary with over 1500 words and a periodic table with extensive element information.
On on-line book covering the concept of pressure, the four major gas laws as they apply to diving, composition of air, changes in gas pressures with depth, ear and sinus squeeze, lung barotrauma, air embolism, decompression sickness, nitrogen narcosis, oxygen toxicity, carbon monoxide and carbon dioxide toxicity, stress, hypothermia, hyperventilation, and oxygen therapy.
www.homeworkhotline.com /Chemistry.htm   (4993 words)

  
 The Math Forum - Math Library - History/Biography   (Site not responding. Last check: 2007-11-01)
Biographies are cross-referenced to articles on the development of mathematical ideas and MacTutor also cross-references stacks in Calculus, Geometry, Algebra (in particular Group Theory), Graph Theory, Number Theory, History of Mathematics, Statistics, Matrices, and Complex Analysis.
Math tools (flash cards, a metric converter); games (magic square), and reference pages: biographies, a glossary, the multiplication table, metric conversion factors, and an ask an expert service.
Algebra and Geometry in Ancient India, where mathematics had its roots in Vedic literature, nearly 4000 years old.
www.mathforum.org /library/topics/history   (3101 words)

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