The name of the specific tensor product "$\boxtimes$" of vector bundles over a Cartesian product of manifolds

Question

Let $M, N$ be smooth (or topological, or algebraic etc.) manifolds and let $E \to M$ and $F \to N$ be two smooth vector bundles. Let $p : M \times N \to M$ and $q : M \times N \to N$ be the natural projections.

Does the vector bundle $E \boxtimes F \to M \times N$ defined as $p^* E \otimes q^* F$ have a name?

Berline, Getzler and Vergne, for instance, introduce it at page 74 of "Heat Kernels and Dirac Operators", but use it across the whole book without giving it any name, so maybe it doesn't have one.

Answer 1

It is called the external tensor product. The same terminology is used in algebraic geometry.