Speaker : Professor Derchyi Wu (Institute of Mathematics, Academia Sinica)
Title : On Twisted integrable hierarchies II
Time : 2011-09-30 (Fri) 16:00 - 17:00
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: Some far-reaching generalizations of the well-known connection between the sine-Gordon equation, the Bcklund transformation, and surfaces with curvature will be derived in the talks. Namely, we will justify that the one-dimensional systems of the twisted -hierarchies for , are the Gauss-Codazzi equation for -dimensional timelike submanifolds with constant sectional curvature and index in pseudo-Euclidean -dimensional space with index and investigate their integrable structures. Peculiar analytical features in the inverse scattering theory of twisted integrable hierarchies are also discussed to solve the Cauchy problem of twisted flows. As a corollary, an existence theorem of these pseudo-Riemannian submanifolds is proved.