MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is the following fact well known?

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 $T^* (X \times V)=T^* X \times V \times V^* =T^* (X \times V^* )$.

I know the proof, but I prefer not to write it in a paper if it is a well known fact.

share|cite|improve this question
I suppose you mean $E_2$ is the annihilator of $E_1$, since it is a subbundle of $X \times V^*$, and since you don't have a metric on $X \times V$ anyway. It's not a long proof, so what does it hurt to write it in the paper if it helps the reader? The worst than can happen is that the referee will ask you to remove it. I wouldn't do that if I was the referee. – Spiro Karigiannis Feb 5 '12 at 1:46

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.