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Feb 5, 2012 at 1:46 comment added Spiro Karigiannis 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.
Feb 4, 2012 at 19:14 history asked Rami CC BY-SA 3.0