Erratum to ``Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson-Walker spacetimes''. (Q5891132)

From the text: The proof of Corollary 4.3 in our paper [ibid. 152, No. 2, 365--383 (2012; Zbl 1241.53051)] is not correct because there is a mistake in the expression given for \(\| X^\ast\wedge Y^\ast\|^2\) on page 374. In fact, the correct expression for this term is NEWLINE\[NEWLINE\begin{aligned} \| X^\ast\wedge Y^\ast\|^2 & =\| X^\ast\|^2\| Y^\ast\|^2-\langle X^\ast,Y^\ast\rangle^2\\& =1+\langle X,T\rangle^2+\langle Y,T\rangle^2\geqslant 1,\end{aligned}NEWLINE\]NEWLINE and then the inequality (4.9) is no longer true. Observe that all the previous reasoning before the wrong expression for \(\| X^\ast\wedge Y^\ast\|^2\) is correct.