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Let $M$ and $N$ be two Riemannian manifolds with Riemannian metrics $g$, $h$ respectively. We consider the product $M \times N$ with metric $g \oplus h$. By the metric we get an isomorphism of bundles $T(M \times N) = TM \times TN$.

My question is: is this also true for the cotangent bundle?

I.e. is $T^{*}(M \times N) = T^{*}M \times T^{*}N$?

I hope for a lot of answers and want to thank in advance.

  • 1
    Why would you need the metric for the isomorphism of the tangent bundles?2012-10-26

1 Answers 1