Erratum to “Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson–Walker spacetimes”. Math. Proc. Camb. Phil. Soc. (2012), 152, 365–383.

Extract

The proof of Corollary 4⋅3 in our paper [1] is not correct because there is a mistake in the expression given for ∥X* ∧ Y*∥² on page 374. In fact, the correct expression for this term is

\begin{eqnarray*} \norm{X^*\wedge Y^*}^2 & = & \norm{X^*}^2\norm{Y^*}^2-\pair{X^*,Y^*}^2\\ {} & = & 1+\pair{X,T}^2+\pair{Y,T}^2\geq 1, \end{eqnarray*}

and then the inequality (4⋅9) is no longer true. Observe that all the previous reasoning before the wrong expression for ∥X* ∧ Y*∥² is correct.