hi,

I have a general question. Assume we have a real analytic $n-$dim. manifold $X$ and $M$ a real analytic compact submanifold of $X$ (of dimension less that the dimension of $X$, say $k < n$). Furthermore assume that on $M$ we have a real analytic $l-$form $\Omega$ ($l < k$). Let $\{U_{i}\}$ be a finite covering of $M$ by open sets in $X$ and on each $U_{i}$ we have a real analytic $l-$form $\alpha_{i}$ which restricted on $M$ is the form $\Omega$. Is it possible to use analycity to glue all forms $\alpha_{i}$ together to get one form $\alpha$ on a neighbourhood of the real manifold $M$?