https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Curve_%28differential_manifold%29 2026-08-10T18:19:21Z Revision history for this page on the wiki MediaWiki 1.41.2 https://diffgeom.subwiki.org/w/index.php?title=Curve_(differential_manifold)&diff=339&oldid=prev 2008-05-18T19:37:22Z

<p>1 revision</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:37, 18 May 2008</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

Vipul https://diffgeom.subwiki.org/w/index.php?title=Curve_(differential_manifold)&diff=338&oldid=prev 2008-04-06T22:33:45Z

<p>New page: ==Definition== In the sense of <a href="/wiki/Differential_manifold" title="Differential manifold">differential manifolds</a>, a curve is a connected one-dimensional differential manifold. Note that this differs somewhat from the notion of a [[curve in Eu...</p> <p><b>New page</b></p><div>==Definition==<br /> <br /> In the sense of [[differential manifold]]s, a curve is a connected one-dimensional differential manifold. Note that this differs somewhat from the notion of a [[curve in Euclidean space]] or a [[curve (Riemannian manifold)]].<br /> <br /> There are two diffeomorphism types of a curve:<br /> <br /> * The real line: This is the non-compact case<br /> * The circle: This is the compact case<br /> <br /> However, there is a wide range of possibilities for a curve as a Riemannian manifold, and an even wider range of possibilities for embeddings in the Euclidean plane. For instance, an embedding of the circle in the Euclidean plane, is equivalent to the notion of a [[simple closed curve in the plane]].</div>

Vipul