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

Published online by Cambridge University Press:  05 June 2013

LUIS J. ALÍAS ,
DEBORA IMPERA  and
MARCO RIGOLI
LUIS J. ALÍAS
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain. e-mail: [email protected]
DEBORA IMPERA
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi 53, I-20125 Milano, Italy. e-mail: [email protected]
MARCO RIGOLI
Affiliation:
Dipartimento di Matematica, Università degli studi di Milano, Via Saldini 50, I-20133 Milano, Italy. e-mail: [email protected]
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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.

Type
Erratum
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 2 , September 2013 , pp. 375 - 377
Copyright
Copyright © Cambridge Philosophical Society 2013 

References

REFERENCE

[1]Alías, L. J., Impera, D. and Rigoli, M.Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson–Walker spacetimes. Math. Proc. Camb. Phil. Soc. 152 (2012), 365–383.CrossRefGoogle Scholar