Open AccessTwistorial maps between quaternionic manifolds
Author(s) -
Stere Ianus,
Stefano Marchiafava,
Ливиу Орнеа,
Radu Pantilie
Publication year - 2010
Publication title -
annali della scuola normale superiore di pisa. classe di scienze
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.444
H-Index - 37
eISSN - 2036-2145
pISSN - 0391-173X
DOI - 10.2422/2036-2145.2010.1.02
Subject(s) - mathematics , quaternionic representation , pure mathematics , rank (graph theory) , geodesic , integrable system , quaternion , mathematical analysis , geometry , combinatorics , irreducible representation , real representation
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 space