BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:CR-twistor spaces over manifolds with G_2- and Spi
n(7)-structures - Hông Vân Lê (Czech Academy of Sc
iences)
DTSTART;TZID=Europe/London:20230222T160000
DTEND;TZID=Europe/London:20230222T170000
UID:TALK194308AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/194308
DESCRIPTION:In 1984\, inspired by Penrose's successful twistor
program\, LeBrun constructed a CR-twistor space o
ver an arbitrary conformal Riemannian 3-manifold
and proved that the CR-structure is formally integ
rable. This twistor construction has been generali
zed by Rossi in 1985 for m-dimensional Riemannian
manifolds endowed with a (m-1)fold vector cross p
roduct (VCP). In 2011 Verbitsky generalized LeBrun
's construction of twistor-spaces to 7-manifolds e
ndowed with a G_2-structure. In my talk I shall r
eport on my joint work with Domenico Fiorenza (arX
iv:2203.04233) on a unification and generalization
of LeBrun's\, Rossi's and Verbitsky's constructio
n to the case where a Riemannian manifold (M\, g)
has a VCP structure. I shall explain how to expre
ss the formal integrability of the CR-structure in
terms of a torsion tensor on the twistor space\
, which is a Grassmanian bundle over (M\, g). If t
he VCP structure on (M\,g) is generated by a G_2-
or Spin(7)-structure\, then the vertical componen
t of the torsion tensor vanishes if and only if (M
\, g) has constant curvature\, and the horizontal
component vanishes if and only if (M\,g) is a tors
ion-free G_2 or Spin(7)-manifold. Finally I shall
discuss some open problems.
LOCATION:MR13
CONTACT:Oscar Randal-Williams
END:VEVENT
END:VCALENDAR