Taiwanese Journal of Mathematics

PARALLEL SURFACES IN THREE-DIMENSIONAL LORENTZIAN LIE GROUPS

Giovanni Calvaruso and Joeri Van der Veken

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Abstract

A three-dimensional homogeneous Lorentzian manifold is either symmetric or locally isometric to a Lie group equipped with a left-invariant Lorentzian metric [4]. We completely classify surfaces with parallel second fundamental form in all non-symmetric homogeneous Lorentzian three-manifolds. Interesting differences arise with respect to the Riemannian case studied in [11, 12].

Article information

Source
Taiwanese J. Math., Volume 14, Number 1 (2010), 223-250.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405737

Digital Object Identifier
doi:10.11650/twjm/1500405737

Mathematical Reviews number (MathSciNet)
MR2603452

Zentralblatt MATH identifier
1194.53019

Subjects
Primary: 53B25: Local submanifolds [See also 53C40] 53C40: Global submanifolds [See also 53B25]

Keywords
parallel second fundamental form surface Lie group Lorentzian manifold

Citation

Calvaruso, Giovanni; Veken, Joeri Van der. PARALLEL SURFACES IN THREE-DIMENSIONAL LORENTZIAN LIE GROUPS. Taiwanese J. Math. 14 (2010), no. 1, 223--250. doi:10.11650/twjm/1500405737. https://projecteuclid.org/euclid.twjm/1500405737


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