Mathematics Seminars at ICTP - Tuesday 14 October

[Math]

M A T H E M A T I C S   S E M I N A R S   2008

Tuesday, 14 October at 14:00 hrs.

Prof. Stefan Ivanov

(Sofia University, Bulgaria)

"Extremals for the Sobolev inequality on the quaternionic Heisenberg  
group and the quaternionic contact Yamabe problem"

Abstract: We describe explicitly non-negative extremals for the  
Sobolev inequality on the seven dimensional quaternionic Hesenberg  
group and determine the best constant in the $L^2$ Folland-Stein  
embedding theorem involving quaternionic contact geometry and the  
Biquard connection. Consequently, we obtain a solution of the  
quaternionic contact Yamabe problem on the quaternionic seven  
sphere.  We show that the torsion of the Biquard connection is the  
only obstruction quaternionic contact structure to be locally  
isomorphic to a 3-Sasakian one. We define a curvature-type tensor  
invariant called quaternionic contact (qc) conformal curvature  in  
terms of the curvature and torsion of the Biquard connection. The  
discovered tensor is similar to the Weyl conformal curvature in  
Riemannian geometry and to the Chern-Moser invariant in CR geometry.  
We show that a quaternionic contact manifold is locally qc conformal  
(gauge equivalent) to the standard flat quaternionic contact  
structure on the quaternionic Heisenberg group, or equivalently, to  
the standard 3-sasakian structure on the sphere if and only if the qc  
conformal curvature vanishes.

Venue:  SEMINAR ROOM, (ICTP Leonardo Building, first floor)