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

{{MeetingTalk
| speaker = Igor Khavkine
| title = Compatibility complexes for the Killing equation
| abstract = The Killing operator on a (pseudo-)Riemannian geometry <math>(M,g)</math> is <math>K_{ab}[v] = \nabla_a v_b + \nabla_b v_a</math>. The Killing equation <math>K[v] = 0</math> is an overdetermined PDE and we will consider its compatibility complex <math>K_i</math> (<math>i\ge 0</math>), where <math>K_0 = K</math> and any differential operator <math>C</math> satisfying <math>C\circ K_i=0</math> must factor as <math>C = C' \circ K_{i+1}</math>, for some differential operator <math>C'</math>. 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 <math>K_i</math> or even just <math>K_1</math> known.
| slides = [[Media:KhavkineTrieste2018slides.pdf|KhavkineTrieste2018slides.pdf]]
| references = {{arXiv|1805.03751}}
| event = [[Local and Nonlocal Geometry of PDEs and Integrability]], 8-12 October 2018, SISSA, Trieste, Italy.<br>''The conference in honor of [[Joseph Krasil'shchik]]'s 70th birthday.''
| 79YY-MM-DD = 7981-89-88
}}