Quaternionic contact structures in dimension 7

David Duchemin[1]

  • [1] Université du Québec à Montréal Centre interuniversitaire de recherche en géométrie différentielle et topologie CP 8888 Succursale centre-ville Montréal (QC) H3C 3P8 (Canada)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 4, page 851-885
  • ISSN: 0373-0956

Abstract

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The conformal infinity of a quaternionic-Kähler metric on a 4 n -manifold with boundary is a codimension 3 distribution on the boundary called quaternionic contact. In dimensions 4 n - 1 greater than 7 , a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7 , we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic-Kähler metric. This allows us to find the quaternionic-contact structures on the 7 -sphere close to the conformal infinity of the quaternionic hyperbolic metric and which are the boundaries of complete quaternionic-Kähler metrics on the 8 -ball. Finally, we construct a 25 -parameter family of Sp ( 1 ) -invariant complete quaternionic-Kähler metrics on the 8 -ball together with the 25 -parameter family of their boundaries.

How to cite

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Duchemin, David. "Quaternionic contact structures in dimension $7$." Annales de l’institut Fourier 56.4 (2006): 851-885. <http://eudml.org/doc/10174>.

@article{Duchemin2006,
abstract = {The conformal infinity of a quaternionic-Kähler metric on a $4n$-manifold with boundary is a codimension $3$ distribution on the boundary called quaternionic contact. In dimensions $4n-1$ greater than $7$, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension $7$, we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic-Kähler metric. This allows us to find the quaternionic-contact structures on the $7$-sphere close to the conformal infinity of the quaternionic hyperbolic metric and which are the boundaries of complete quaternionic-Kähler metrics on the $8$-ball. Finally, we construct a $25$-parameter family of Sp$(1)$-invariant complete quaternionic-Kähler metrics on the $8$-ball together with the $25$-parameter family of their boundaries.},
affiliation = {Université du Québec à Montréal Centre interuniversitaire de recherche en géométrie différentielle et topologie CP 8888 Succursale centre-ville Montréal (QC) H3C 3P8 (Canada)},
author = {Duchemin, David},
journal = {Annales de l’institut Fourier},
keywords = {contact structures; quaternionic-kähler metrics; twistor spaces; quaternionic Kähler metrics},
language = {eng},
number = {4},
pages = {851-885},
publisher = {Association des Annales de l’institut Fourier},
title = {Quaternionic contact structures in dimension $7$},
url = {http://eudml.org/doc/10174},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Duchemin, David
TI - Quaternionic contact structures in dimension $7$
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 4
SP - 851
EP - 885
AB - The conformal infinity of a quaternionic-Kähler metric on a $4n$-manifold with boundary is a codimension $3$ distribution on the boundary called quaternionic contact. In dimensions $4n-1$ greater than $7$, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension $7$, we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic-Kähler metric. This allows us to find the quaternionic-contact structures on the $7$-sphere close to the conformal infinity of the quaternionic hyperbolic metric and which are the boundaries of complete quaternionic-Kähler metrics on the $8$-ball. Finally, we construct a $25$-parameter family of Sp$(1)$-invariant complete quaternionic-Kähler metrics on the $8$-ball together with the $25$-parameter family of their boundaries.
LA - eng
KW - contact structures; quaternionic-kähler metrics; twistor spaces; quaternionic Kähler metrics
UR - http://eudml.org/doc/10174
ER -

References

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