Conformal Killing-Yano 2-forms on Lie groups

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

Petrolina

Congreso; V Latin American Conference on Lie groups and Geometry; 2014

Universidade Federal do Vale do São Francisco

Killing-Yano p-forms were first introduced by Kentaro Yano in 1952 as a natural generalization of ordinary Killing vector fields. They have been intensively studied by physicists since the work of R. Penrose-M.Walker (1970). Killing-Yano tensors give rise to quadratic first integrals of the geodesic equation and allow to define operators which commute or anti-commute with the Dirac operator on the manifold. Conformal Killing-Yano tensors, a generalization of conformal Killing vector fields, have been applied to define symmetries of field equations. We consider left invariant conformal Killing-Yano 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 bi-invariant metric. In dimension 3, we obtain the classification of the Lie groups and the left invariant metrics admitting conformal Killing-Yano 2-forms.