most recent 30 from http://mathoverflow.net 2013-05-21T06:33:56Z http://mathoverflow.net/feeds/user/2818 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/9824/is-the-volume-form-on-an-oriented-riemannian-manifold-parallel Dan 2009-12-26T20:35:08Z 2011-12-03T13:27:34Z

<p>This question actually has two parts:</p> <ol> <li><p>Am I correct that the Riemannian connection induces a connection on the k-th exterior power of the cotangent bundle, for any k? What I had in mind was: view the Riemannian connection as a connection on the frame bundle and then think of the k-th exterior power of the cotangent bundle as the associated bundle to the frame bundle under the natural action of GL(n) on the k-th exterior algebra of (R^n)*. </p></li> <li><p>If you view the volume form of an oriented Riemannian manifold as a section of the n-th exterior power of the cotangent bundle, is it always parallel with respect to this connection?</p></li> </ol>