Khavkine I. Compatibility complexes for the Killing equation (abstract)

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Speaker: Igor Khavkine

Title: Compatibility complexes for the Killing equation

Abstract:
The Killing operator on a (pseudo-)Riemannian geometry (M,g) is Kab[v]=avb+bva. The Killing equation K[v]=0 is an overdetermined PDE and we will consider its compatibility complex Ki (i0), where K0=K and any differential operator C satisfying CKi=0 must factor as C=CKi+1, for some differential operator C. 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 Ki or even just K1 known.

Slides: KhavkineTrieste2018slides.pdf

References:
arXiv:1805.03751

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.