Conformal Killing 2-forms on 4-dimensional manifolds

A. ANDRADA; BARBERIS, M.L.; MOROIANU, A.

Campinas

Workshop; IV School and Workshop on Lie Theory; 2015

IMECC-UNICAMP

Conformal Killing forms were introduced a few decades ago in the physicsliterature as a way to construct first integrals of the equation of motion. Con-formal Killing forms generalize to higher degrees the notion of conformal vec-tor fields, and can be characterized by the fact that their covariant derivativewith respect to the Levi-Civita connection is completely determined by theirexterior derivative and divergence. In this talk we will be mainly concernedwith conformal Killing 2-forms on 4-dimensional Riemannian manifolds, andin particular we will describe all metric Lie algebras of dimension 4 whoseassociated simply connected Lie groups G endowed with the correspondingleft-invariant Riemannian metric carry non-trivial conformal Killing 2-forms.Joint work with Adrian Andrada and Andrei Moroianu.