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Isometric immersions into a homogeneous Lorentzian Heisenberg group and rigidity

Published online by Cambridge University Press:  01 July 2009

SINUÊ DAYAN BARBERO LODOVICI  and
FERNANDO MANFIO
SINUÊ DAYAN BARBERO LODOVICI
Affiliation:
Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, CEP 05508-900, São Paulo, SP, Brazil. e-mail: [email protected] and [email protected]
FERNANDO MANFIO
Affiliation:
Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, CEP 05508-900, São Paulo, SP, Brazil. e-mail: [email protected] and [email protected]
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Abstract

In this paper we prove an existence result for local and global isometric immersions of semi-Riemannian surfaces into the three dimensional Heisenberg group endowed with a homogeneous left–invariant Lorentzian metric. As a corollary, we prove a rigidity result for such immersions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 1 , July 2009 , pp. 185 - 204
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

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