https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Conjugate_points 2026-08-28T16:16:31Z Revision history for this page on the wiki MediaWiki 1.41.2 https://diffgeom.subwiki.org/w/index.php?title=Conjugate_points&diff=179&oldid=prev 2008-05-18T19:34:56Z

<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 19:34, 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=Conjugate_points&diff=178&oldid=prev 2007-04-23T15:25:25Z

<p></p> <p><b>New page</b></p><div>==Definition==<br /> <br /> A pair of points in a Riemannian manifold are said to be &#039;&#039;&#039;conjugate points&#039;&#039;&#039; if there is a [[Jacobi field]] that vanishes at both points. In other words, we can construct a geodesic variation of a geodesic joining the two points, or there is a smoothly varying infinite family of geodesics joining the two points.<br /> <br /> To any pair of conjugate points, we can associate a corresponding multiplicity, which is the nullity of a certain space associated with the energy functional.<br /> <br /> If a Riemannian manifold has negative sectional curvature everywhere then there does not exist any pair of conjugate points.</div>

Vipul