= Tensor bundle
{title2=$T^r_sM$}
For a <smooth manifold> $M$, the tensor bundle $T^r_sM=(TM)^{\otimes r}\otimes(T^*M)^{\otimes s}$ is a <vector bundle> whose smooth <sections of a vector bundle> are <tensor fields> of type $(r,s)$. Its <transition functions of a vector bundle> are tensor products of the <tangent bundle> transition matrices and their inverse transposes. <Symmetric tensors> and <differential forms> arise from the symmetric and alternating subbundles.
// Target: fiber-bundle.bigb
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