https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Diffgeom%3APurpose_statement 2026-07-09T20:36:52Z Revision history for this page on the wiki MediaWiki 1.41.2 https://diffgeom.subwiki.org/w/index.php?title=Diffgeom:Purpose_statement&diff=1677&oldid=prev 2008-05-18T20:13:35Z

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Vipul https://diffgeom.subwiki.org/w/index.php?title=Diffgeom:Purpose_statement&diff=1676&oldid=prev 2007-05-26T07:04:29Z

<p></p> <p><b>New page</b></p><div>{{diffgeom}}<br /> <br /> This page describes what the basic purpose of diffgeom is. It is written by [[User:Vipul|Vipul Naik]], the person currently running the wiki.<br /> <br /> ==The motivation behind diffgeom==<br /> <br /> Diffgeom has been started on an experimental basis to mimic many of the successful features of the [http://groupprops.wiki-site.com/ Group properties wiki]. By &#039;&#039;successful&#039;&#039; is meant features on the Group properties wiki that seem to make for systematic and powerful documentation. In particular, Diffgeom hopes to be an active repository of definitions, facts, proofs and motivational material in the theory of differential manifolds, Riemannian manifolds, differential topology, symplectic/contact geometry, and related subjects. Diffgeom aims to be:<br /> <br /> * A quick reference tool for gathering the basic definition and important properties of any term/concept<br /> * A quick tool to check whether a particular fact (in differential geometry) is true, and to find facts related to a particular term<br /> * A quick tool to understand the proof of a result and figure out whether that proof is applicable in other contexts<br /> * A place where one can read articles motivating the development of any term or concept, as well as survey articles explaining the application of a principle or idea or related cluster of ideas<br /> <br /> ==Diffgeom vis-a-vis other reference tools==<br /> <br /> ===Diffgeom versus Groupprops===<br /> <br /> Diffgeom is very much inspired by the Groupprops effort, but it seeks to be different in a number of ways. First of all it does &#039;&#039;not&#039;&#039; work on the same organizational principles as Groupprops. For instance, the property-theoretic scheme of classification works very well in group theory, but is not likely to work so well in differential geometry (because of the more continuous nature of differential geometry). So while we &#039;&#039;do&#039;&#039; make use of the property-theoretic paradigm we also use a number of other [[Diffgeom:Organizational principle|organizational principles and paradigms]]<br /> <br /> ===Diffgeom versus Wikipedia===<br /> <br /> Wikipedia is currently one big huge place where you can get everything -- and currently, of course the Wikipedia articles on differential geometry will be far more comprehensive, informative and well-written than those on Diffgeom. However, there are a number of niches where Diffgeom can and will overtake Wikipedia, or for that matter, any general-purpose encyclopaedia. If it is not clear how this is going to happen, check out [http://groupprops.wiki-site.com/index.php/Groupprops:Groupprops_versus_Wikipedia Groupprops versus Wikipedia] for a comparison between a small-scale enterprise like this one, and something huge like Wikipedia.<br /> <br /> ===Diffgeom versus other reference tools===<br /> <br /> We are currently too small to comment, but hopefully there will be something to say here after some time!</div>

Vipul