Conformal Killing 2-forms on low dimensional Lie groups

A. ANDRADA; BARBERIS, M.L.; I. DOTTI

Bedlewo

Workshop; Workshop on almost hermitian and contact geometry; 2015

Conformal Killing forms were introduced a few decades ago in the physics literature as a way toconstruct first integrals of the equation of motion. Conformal Killing forms generalize to higherdegrees the notion of conformal vector fields, and can be characterized by the fact that theircovariant derivative with respect to the Levi-Civita connection is completely determined by theirexterior derivative and divergence. Such forms have been applied to define symmetries of fieldequations.We consider left invariant conformal Killing 2-forms on Lie groups with a left invariant metric.We present some results for 2-step nilpotent Lie groups and for compact Lie groups with a biinvariantmetric. In dimension 3, we obtain the classification of the Lie groups and the leftinvariant metrics admitting conformal Killing-Yano 2-forms. In the 4-dimensional case, we obtainsome general results for Riemanniana manifolds and we consider conformal Killing 2-forms (notnecessarily left invariant) on 4-dimensional Lie groups. We describe all metric Lie algebras ofdimension 4 whose associated simply connected Lie groups G endowed with the correspondingleft-invariant Riemannian metric carry non-trivial conformal Killing 2-forms.