https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Injectivity_radius_of_a_manifold 2026-09-05T17:27:51Z Revision history for this page on the wiki MediaWiki 1.41.2 https://diffgeom.subwiki.org/w/index.php?title=Injectivity_radius_of_a_manifold&diff=748&oldid=prev 2008-05-18T19:47:17Z

<p>2 revisions</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 19:47, 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=Injectivity_radius_of_a_manifold&diff=747&oldid=prev 2007-04-25T08:53:12Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:53, 25 April 2007</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{scalar value}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{scalar value <ins style="font-weight: bold; text-decoration: none;">on riemannian manifold</ins>}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition==</div></td></tr> </table>

Vipul https://diffgeom.subwiki.org/w/index.php?title=Injectivity_radius_of_a_manifold&diff=746&oldid=prev 2007-04-08T12:55:03Z

<p></p> <p><b>New page</b></p><div>{{scalar value}}<br /> <br /> ==Definition==<br /> <br /> The &#039;&#039;&#039;injectivity radius&#039;&#039;&#039; of a [[Riemannian manifold]] is defined as the infimum over all points, of the [[injectivity radius]] at that point.<br /> <br /> ==Facts==<br /> <br /> ===Klingenberg&#039;s theorem===<br /> <br /> {{further|[[Klingenberg&#039;s theorem]]}}<br /> <br /> A useful way of bounding the injectivity radius of a manifold is the so-called [[Klingenberg&#039;s theorem]] which states that the injectivity radius of the manifold is bounded from below by the minimum of two values, one being inversely related to any upper bound on sectional curvature, and the other being related to the minimum length of a smooth closed geodesic.</div>

Vipul