Seminar talk, 11 October 2023

From Geometry of Differential Equations
Revision as of 19:58, 7 September 2023 by Verbovet (talk | contribs) (Created page with "{{Talk | speaker = Boris Doubrov | title = Extrinsic geometry and linear differential equations of SL(3)-type | abstract = As an application of the general theory on extrinsic geometry, we investigate extrinsic geometry of submanifolds in flag varieties and systems of linear PDEs for a class of special interest associated with the adjoint representation of SL(3). It may be seen as a contact generalization of the classical description of surfaces in P^3 in terms of two li...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

Speaker: Boris Doubrov

Title: Extrinsic geometry and linear differential equations of SL(3)-type

Abstract:
As an application of the general theory on extrinsic geometry, we investigate extrinsic geometry of submanifolds in flag varieties and systems of linear PDEs for a class of special interest associated with the adjoint representation of SL(3). It may be seen as a contact generalization of the classical description of surfaces in P^3 in terms of two linear PDEs of second order.

We carry out a complete local classification of the homogeneous structures in this class. As a result, we find 7 kinds of new systems of linear PDE's of second order on a 3-dimensional contact manifold each of which has a solution space of dimension 8. Among them there are included a system of PDE's called contact Cayley's surface and one which has SL(2) symmetry.

Retrieved from "https://gdeq.org/index.php?title=Seminar_talk,_11_October_2023&oldid=7055"