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Twistorial maps between quaternionic manifolds. (English) Zbl 1193.53121
Authors’ abstract: We introduce a natural notion of quaternionic map between almost quaternionic manifolds and we prove the following, for maps of rank at least one:
\(\bullet\) A map between quaternionic manifolds endowed with an integrable almost twistorial structure is twistorial if and only if it is quaternionic.
\(\bullet\) A map between quaternionic manifolds endowed with a nonintegrable almost twistorial structure is twistorial if and only if it is quaternionic and totally-geodesic.
As an application, we describe all quaternionic maps between open sets of quaternionic projective spaces.

MSC:
53C28 Twistor methods in differential geometry
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
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