What is the expression for the tangent bundle of the open positive orthant $\mathbb R_+^n$? I think I know the answer, but just to be sure. Thanks
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1Well it's diffeomorphic to $\Bbb R^n$ so as a bundle its just the trivial bundle $\Bbb R^n\times M \to M$. In general if $M \subset \Bbb R^n$ with $M$ open in $\Bbb R^n$, $TM$ is just the pullback of $T \Bbb R^n$ along the inclusion (which is also always trivial as a bundle). – PVAL-inactive Sep 02 '15 at 23:55
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@PVAL Thanks, that what I have expected. What about the tangent bundle for the close positive orthant? – M.A Sep 03 '15 at 09:37