most recent 30 from http://mathoverflow.net 2013-05-21T08:32:06Z http://mathoverflow.net/feeds/question/73268 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/73268/jet-spaces-for-maps-with-constraints Mirco 2011-08-20T09:43:41Z 2011-08-21T09:44:52Z

<p>Lets be in the category $\mathbf{M}$ of smooth finite dimensional manifolds with smooth maps:</p> <p>Suppose we have the set of all smooth maps $Hom_\mathbf{M}(R^n,M)$ from $R^n$ to a smooth manifold $M$. Taking only the first Taylor-Approximation of any such map, gives us the n-velocity Space $T_nM$, that is a fiber bundle over $M$ and a generalization of $TM$.</p> <p>Now suppose we just have a subset of $Hom(R^n,M)$ given by some constraints on the maps lets say $$Hom_\mathbf{M}( R^n,M | constraint_1(f) ... constraint_n(f) )$$. </p> <p>Does this always gives us a subbundle of $T_nM$? </p> <p>If not, what should be required to be a subbundle? </p> <p>Or say it the other way around: What must we proof, to show that the appropriate Jet set is a subbundle of $T_nM$?</p> <p>(For my purposes its enough to suppose, that the constraints are of zero-order i.e. don't involve any derivations)</p>