Twistorial maps between quaternionic manifolds
Differential Geometry
2015-05-13 v2
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: 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.
Cite
@article{arxiv.0801.4587,
title = {Twistorial maps between quaternionic manifolds},
author = {S. Ianus and S. Marchiafava and L. Ornea and R. Pantilie},
journal= {arXiv preprint arXiv:0801.4587},
year = {2015}
}
Comments
Minor improvements and two references added for Definition 2.7 and Proposition 2.8