Khavkine I. Compatibility complexes for the Killing equation (abstract)
Speaker: Igor Khavkine
Title: Compatibility complexes for the Killing equation
The Killing operator on a (pseudo-)Riemannian geometry is . The Killing equation is an overdetermined PDE and we will consider its compatibility complex (), where and any differential operator satisfying must factor as , for some differential operator . Relying on the "finite-type" property of K, I will discuss a practical construction of such a compatibility complex on geometries of sub-maximal symmetry, with examples coming from General Relativity. Prior to this work, there were very few examples with the full compatibility complex or even just known.
Event: Local and Nonlocal Geometry of PDEs and Integrability, 8-12 October 2018, SISSA, Trieste, Italy.
The conference in honor of Joseph Krasil'shchik's 70th birthday.