We introduce a natural notion of quaternionic map between almost quaternionic manifolds and we prove the following, for maps of rank at least one: - A map between quaternionic manifolds endowed with the integrable almost twistorial structures is twistorial if and only if it is quaternionic. - 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 all the quaternionic maps between open sets of quaternionic projective spaces.
Ianuş, Stere 1 ; Marchiafava, Stefano 2 ; Ornea, Liviu 1, 3 ; Pantilie, Radu 3
@article{ASNSP_2010_5_9_1_47_0,
author = {Ianu\c{s}, Stere and Marchiafava, Stefano and Ornea, Liviu and Pantilie, Radu},
title = {Twistorial maps between quaternionic manifolds},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {47--67},
year = {2010},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 9},
number = {1},
mrnumber = {2668873},
zbl = {1193.53121},
language = {en},
url = {https://www.numdam.org/item/ASNSP_2010_5_9_1_47_0/}
}
TY - JOUR AU - Ianuş, Stere AU - Marchiafava, Stefano AU - Ornea, Liviu AU - Pantilie, Radu TI - Twistorial maps between quaternionic manifolds JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 47 EP - 67 VL - 9 IS - 1 PB - Scuola Normale Superiore, Pisa UR - https://www.numdam.org/item/ASNSP_2010_5_9_1_47_0/ LA - en ID - ASNSP_2010_5_9_1_47_0 ER -
%0 Journal Article %A Ianuş, Stere %A Marchiafava, Stefano %A Ornea, Liviu %A Pantilie, Radu %T Twistorial maps between quaternionic manifolds %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 47-67 %V 9 %N 1 %I Scuola Normale Superiore, Pisa %U https://www.numdam.org/item/ASNSP_2010_5_9_1_47_0/ %G en %F ASNSP_2010_5_9_1_47_0
Ianuş, Stere; Marchiafava, Stefano; Ornea, Liviu; Pantilie, Radu. Twistorial maps between quaternionic manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 1, pp. 47-67. https://www.numdam.org/item/ASNSP_2010_5_9_1_47_0/
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