Co-normal bundle of orthogonal compliment - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T15:50:39Z http://mathoverflow.net/feeds/question/87543 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/87543/co-normal-bundle-of-orthogonal-compliment Co-normal bundle of orthogonal compliment Rami 2012-02-04T19:14:21Z 2012-02-04T19:14:21Z <p>Is the following fact well known?</p> <p>Let $X$ be a manifold and $V$ be a vector space. Let $E_1$ be a sub-bundle of the constant bundle $X \times V$. Let $E_2$ be its orthogonal compliment in $X \times V^*$. Then the co-normal bundle of the total space of $E_1$ inside $X \times V$ coincides with the co-normal bundle of the total space of $E_2$ inside $X \times V^*$, under the identification $T^* (X \times V)=T^* X \times V \times V^* =T^* (X \times V^* )$.</p> <p>I know the proof, but I prefer not to write it in a paper if it is a well known fact.</p>