Erratum to “Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson–Walker spacetimes”. Math. Proc. Camb. Phil. Soc. (2012), 152, 365–383
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Medientyp:
E-Artikel
Titel:
Erratum to “Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson–Walker spacetimes”. Math. Proc. Camb. Phil. Soc. (2012), 152, 365–383
Beteiligte:
ALÍAS, LUIS J.;
IMPERA, DEBORA;
RIGOLI, MARCO
Erschienen:
Cambridge University Press (CUP), 2013
Erschienen in:Mathematical Proceedings of the Cambridge Philosophical Society
Beschreibung:
<jats:p>The proof of Corollary 4⋅3 in our paper [<jats:bold>1</jats:bold>] is not correct because there is a mistake in the expression given for ∥<jats:italic>X</jats:italic>* ∧ <jats:italic>Y</jats:italic>*∥<jats:sup>2</jats:sup> on page 374. In fact, the correct expression for this term is
<jats:disp-formula-group><jats:disp-formula><jats:alternatives><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" orientation="portrait" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0305004113000376_eqnU1" /><jats:tex-math>\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*}</jats:tex-math></jats:alternatives></jats:disp-formula></jats:disp-formula-group>
and then the inequality (4⋅9) is no longer true. Observe that all the previous reasoning before the wrong expression for ∥<jats:italic>X</jats:italic>* ∧ <jats:italic>Y</jats:italic>*∥<jats:sup>2</jats:sup> is correct.</jats:p>