Twistorial maps between quaternionic manifolds

Ianuş, Stere; Marchiafava, Stefano; Ornea, Liviu; Pantilie, Radu

Ianuş, Stere ¹ ; Marchiafava, Stefano ² ; Ornea, Liviu ^1,³ ; Pantilie, Radu ³

¹ Universitatea din Bucureşti, Facultatea de Matematică, Str. Academiei n. 14, 70109, Bucureşti, România
² Dipartimento di Matematica, Istituto “Guido Castelnuovo”, Sapienza Università di Roma, Piazzale Aldo Moro, 2, I 00185 Roma, Italia
³ Institutul de Matematică “Simion Stoilow”, al Academiei Române, C.P. 1-764, 014700, Bucureşti, România

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 1, pp. 47-67.

Résumé

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.

MR Zbl

Classification : 53C28, 53C26

Affiliations des auteurs :

Ianuş, Stere ¹ ; Marchiafava, Stefano ² ; Ornea, Liviu ^{1, 3} ; Pantilie, Radu ³

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     title = {Twistorial maps between quaternionic manifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {47--67},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 9},
     number = {1},
     year = {2010},
     mrnumber = {2668873},
     zbl = {1193.53121},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2010_5_9_1_47_0/}
}

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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. http://www.numdam.org/item/ASNSP_2010_5_9_1_47_0/

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