Seminar talk, 11 October 2023: Difference between revisions
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| 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. | | 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.| video = | 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. | ||
| video = | |||
| slides = | | slides = | ||
| references = {{arXiv|2308.06169}} | | references = {{arXiv|2308.06169}} | ||
| 79YY-MM-DD = 7976-89-88 | | 79YY-MM-DD = 7976-89-88 | ||
}} | }} | ||
Revision as of 21:37, 11 October 2023
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.
References:
arXiv:2308.06169