We investigate quaternionic contact (qc) manifolds from the point of view of intrinsic torsion. We argue that the natural structure group for this geometry is a non-compact Lie group K containing Sp(n)ℍ∗, and show that any qc structure gives rise to a canonical K-structure with constant intrinsic torsion, except in seven dimensions, when this condition is equivalent to integrability in the sense of Duchemin. We prove that the choice of a reduction to Sp(n)ℍ∗ (or, equivalently, a complement of the qc distribution) yields a unique K-connection satisfying natural conditions on torsion and curvature. We show that the choice of a compatible metric on the qc distribution determines a canonical reduction to Sp(n)Sp(1) and a canonical Sp(n)Sp(1)-connection whose curvature is almost entirely determined by its torsion. We show that its Ricci tensor, as well as the Ricci tensor of the Biquard connection, has an interpretation in terms of intrinsic torsion.

Conti, D. (2016). Intrinsic torsion in quaternionic contact geometry. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 16(2), 625-674 [10.2422/2036-2145.201407_004].

Intrinsic torsion in quaternionic contact geometry

CONTI, DIEGO
Primo
2016

Abstract

We investigate quaternionic contact (qc) manifolds from the point of view of intrinsic torsion. We argue that the natural structure group for this geometry is a non-compact Lie group K containing Sp(n)ℍ∗, and show that any qc structure gives rise to a canonical K-structure with constant intrinsic torsion, except in seven dimensions, when this condition is equivalent to integrability in the sense of Duchemin. We prove that the choice of a reduction to Sp(n)ℍ∗ (or, equivalently, a complement of the qc distribution) yields a unique K-connection satisfying natural conditions on torsion and curvature. We show that the choice of a compatible metric on the qc distribution determines a canonical reduction to Sp(n)Sp(1) and a canonical Sp(n)Sp(1)-connection whose curvature is almost entirely determined by its torsion. We show that its Ricci tensor, as well as the Ricci tensor of the Biquard connection, has an interpretation in terms of intrinsic torsion.
Articolo in rivista - Articolo scientifico
Intrinsic torsion, quaternionic contact, Biquard connection
English
2016
16
2
625
674
partially_open
Conti, D. (2016). Intrinsic torsion in quaternionic contact geometry. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 16(2), 625-674 [10.2422/2036-2145.201407_004].
File in questo prodotto:
File Dimensione Formato  
qc.pdf

accesso aperto

Tipologia di allegato: Submitted Version (Pre-print)
Dimensione 452.59 kB
Formato Adobe PDF
452.59 kB Adobe PDF Visualizza/Apri
Conti - Intrinsic torsion in quaternionic contact geometry.pdf

Solo gestori archivio

Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Dimensione 1.04 MB
Formato Adobe PDF
1.04 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/134946
Citazioni
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
Social impact