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SUMMARY:Ryushi GOTO (Osaka University)
DTSTART:20210712T010000Z
DTEND:20210712T015000Z
DTSTAMP:20260423T024539Z
UID:2021PRCSG/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/2021PRCSG/1/
 ">Scalar curvature and moment map in Generalized Kähler geometry</a>\nby 
 Ryushi GOTO (Osaka University) as part of 2021 Pacific Rim Complex & Sympl
 ectic Geometry Conference\n\n\nAbstract\nWe introduce a notion of scalar c
 urvature of a twisted generalized Kähler manifold in terms of pure spinor
 s formalism. A moment map framework on an arbitrary compact twisted genera
 lized Kähler manifold is provided and then it turns out that a moment map
  is given by the scalar curvature under the certain condition\, which is a
  generalization of the result of the scalar curvature as a moment map in t
 he ordinary Kähler geometry\, due to Fujiki and Donaldson. A noncommutati
 ve compact Lie group  G  does not have any Kähler structure. However\, we
  show that a compact Lie group has a family of generalized Kähler structu
 res twisted by the Cartan  3-form\, which is constructed by the action of 
 the real Pin group of the double of Cartan subalgebra. Then we show that a
 n arbitrary compact Lie group admits generalized Kähler structures with c
 onstant scalar curvature. In particular\, generalized Kähler structures w
 ith constant scalar curvature on the standard Hopf surface are explicitly 
 given.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/1/
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