Mathematics Seminar on Wednesday, 14 March

[math]

MATHEMATICS SEMINARS - 2012

Wednesday, 14 March, at 14:30 hrs

Dr. Joseph Malkoun
(Notre Dame University-Louaize, Lebanon/ICTP)

"Hyperkahler Geometry, Quaternionic isometries and the Legendre transform"

Abstract: In dimension 4, Anti-self-dual Ricci-flat manifolds play an
important role both in geometry and physics, in particular in general 
relativity. Hyperkahler manifolds are their higher dimensional 
analogues, which exist in dimension 4n, and have restricted holonomy a 
subgroup of Sp(n). If G is an abelian Lie group of dimension n acting
on a hyperkahler 4n-manifold (M,g) by triholomorphic isometries, then it
is well known that the Legendre transform F of a Kahler potential H with 
respect to the moment functions of the action satisfies the system:

F_{x^i x^j} + F_{y^i y^j} + F_{z^i z^j} = 0,   for 1 <= i,j <= n

In this work in progress based on my thesis, we study the effect of an
abelian Lie group G acting on a hyperkahler manifold (M,g) by 
quaternionic isometries, which are more general isometries than the 
triholomorphic ones.
Under reasonable assumptions, if G is n+1-dimensional, we obtain a
reduction of the above linear system by a U(1)-action.
We wish to study as well in the future the case where G is
1-dimensional, which is related to A. Haydys's work.

Venue: Luigi Stasi Seminar Room, ICTP Leonardo Building, first floor.