Speaker:Nie Zhaohu, Utah State University

Date:May 14, 2014

Time:2:30 p.m. - 3:30 p.m.

Location:Room B924, Zhixin Building, Central Campus

Sponsor:School of Mathematics

Abstract：This is a joint work with I. Anderson and P. Nurowski. A parabolic geometry, with the classical examples of conformal geometry, projective geometry and $CR$-geometry, is defined by means of a choice of a parabolic subalgebra in a simple Lie algebra. In particular, the geometry of the (2, 3, 5) distributions on a 5-manifold is the parabolic geometry associated to the simple Lie algebra ${\frak g}_2$ with the parabolic subalgebra defined by the first simple root. Associated with the flat model for this geometry there is a natural underdetermined ODE, the celebrated Hilbert-Cartan equation $\frac{dz}{dx} = (\frac{d^2 y}{dx^2})^2$. In this talk, we will generalize the above example of parabolic geometry to all simple Lie algebras in the framework of non-rigid parabolic geometry of Monge type. The differential equations for the corresponding flat models are all underdetermined systems of ODE’s. A parabolic geometry is called non-rigid if it allows curved analogs, and the non-rigidity is characterized by the second Lie algebra cohomology. For the non-rigid parabolic geometries of Monge type, the ODE systems have particularly simple forms.

For further information, please visit:

http://www.maths.sdu.edu.cn/non-rigid-parabolic-geometries-of-monge-type.html