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 K_{ab}[v] = \nabla_a v_b + \nabla_b v_a. The Killing equation K[v] = 0 is an overdetermined PDE and we will consider its compatibility complex K_i (i\ge 0), where K_0 = K and any differential operator C satisfying C\circ K_i=0 must factor as C = C' \circ K_{i+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 K_i or even just K_1 known.

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.