Twistorial maps between quaternionic manifolds

Details Twistorial maps between quaternionic manifolds Twistorial maps between quaternionic manifolds

2008-01-30

arxiv.org/abs/0801.4587v2

Mathematics

Differential Geometry

Minor improvements and two references added for Definition 2.7 and Proposition 2.8

Scientific paper

We introduce a natural notion of quaternionic map between almost quaternionic manifolds and we prove the following, for maps of rank at least one: 1) A map between quaternionic manifolds endowed with the integrable almost twistorial structures is twistorial if and only if it is quaternionic. 2) A map between quaternionic manifolds endowed with the nonintegrable almost twistorial structures is twistorial if and only if it is quaternionic and totally-geodesic. As an application, we describe the quaternionic maps between open sets of quaternionic projective spaces.

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