On the biharmonic curves in the special linear group $SL(2,R)$
  We characterize the biharmonic curves in the special linear group $SL(2,R)$. In particular, we show that all proper biharmonic curves in $SL(2,R)$are helices and we give their explicit parametrizations as curves in the pseudo-Euclidean space $R^4_2$. 
I.I. Onnis, A. Passos Passamani
math.DG