Left-invariant conformal Killing-Yano 2-forms on Lie groups

ADRIÁN ANDRADA

Zaragoza

Jornada; IUMA day On Special Structures in Geometry; 2014

Universidad de Zaragoza

In this work we study Lie groups equipped with left-invariant Riemannian metrics that admit left-invariant conformal Killing-Yano 2-forms. Firstly we show that if a Lie group admits a strict CKY 2-form, then the dimension of the group is odd. We also provide a construction to obtain examples of left-invariant CKY 2-forms on Lie groups beginning with an even-dimensional Lie group equipped with a non-degenerate parallel 2-form. Next we provide the classication of all 3-dimensional Lie groups equipped with such tensors, and we obtain that in this dimension any left-invariant KY tensor is parallel. We show that if a nilpotent Lie group admits a strict conformal Killing-Yano 2-form, then the group is isomorphic to the (2n+1)-dimensional Heisenberg group. In the compact case, we show that the only compact Lie group equipped with a bi-invariant metric that admits strict CKY 2-forms is SU(2). Moreover, a left-invariant metric g on SU(2) admits such 2-forms if and only if g is homothetic to a Berger metric on the sphere S^3.