Invariant solutions to the conformal Killing-Yano equation on Lie groups

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

JOURNAL OF GEOMETRY AND PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2015 vol. 94 p. 199 - 208

0393-0440

We search for invariant solutions of the conformal Killing-Yano equation on Lie groups equipped with left invariant Riemannian metrics, focusing on $2$-forms. We show that when the Lie group is compact equipped with a bi-invariant metric or $2$-step nilpotent, the only invariant solutions occur on the $3$-dimensional sphere or on a Heisenberg group. We classify the $3$-dimensional Lie groups with left invariant metrics carrying invariant conformal Killing-Yano $2$-forms.