EVENT DETAILS AND ABSTRACT


Analysis Seminar

Title: On the isometric immersion of pseudo-spherical surfaces via evolution and hyperbolic equations
Speaker: Nabil Kahouadji
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

On one hand, the class of PDEs describing pseudo-spherical surfaces, which has been defined and studied in depth in a foundational paper by Chern and Tenenblat, contains a large subclass of equations enjoying remarkable integrability properties, such as the existence of infinite hierarchies of conservation laws, B├Ącklund transformations and associated linear problems, and have been completely classified. On the other hand, a classical theorem in the theory of surfaces states that any pseudo-spherical surface can be locally isometrically immersed into a three-dimensional Euclidean space. This theorem is however largely an existence result, which does not give an explicit expression for the second fundamental form of the local isometric immersion.

I will report on a recent joint work with Niky Kamran and Keti Tenenblat on the classification of the equations describing pseudo-spherical surfaces, for which the components of the second fundamental form of the local isometric immersion depend on a jet of finite order of u.

These results will show among other things that, when viewed through the prism of the local isometric immersions associated to solutions, one equation occupies a special position within the class of equations describing pseudo-spherical surfaces.

Date: Monday, November 12, 2012
Time: 4:10pm
Where: Lunt 105
Contact Person: Dean Baskin
Contact email: dbaskin@math.northwestern.edu
Contact Phone:
Copyright © 1997-2024 Department of Mathematics, Northwestern University.