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LORENTZIAN BCV SPACES: PROPERTIES AND GEOMETRY OF THEIR SURFACES

Part of: Local differential geometry Global differential geometry

Published online by Cambridge University Press:  25 July 2025

GIOVANNI CALVARUSO Open the ORCID record for GIOVANNI CALVARUSO [Opens in a new window]  and
LORENZO PELLEGRINO Open the ORCID record for LORENZO PELLEGRINO [Opens in a new window]
GIOVANNI CALVARUSO*
Affiliation:
Dipartimento di Matematica e Fisica ‘E. De Giorgi’ https://ror.org/03fc1k060Università del Salento, Prov. Lecce-Arnesano, 73100 Lecce, Italy
LORENZO PELLEGRINO
Affiliation:
Dipartimento di Matematica e Fisica ‘E. De Giorgi’ https://ror.org/03fc1k060Università del Salento, Prov. Lecce-Arnesano, 73100 Lecce, Italy e-mail: lorenzo.pellegrino@unisalento.it
*
e-mail: giovanni.calvaruso@unisalento.it
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Abstract

We investigate the Lorentzian analogues of Riemannian Bianchi–Cartan–Vranceanu spaces. We provide their general description and emphasize their role in the classification of three-dimensional homogeneous Lorentzian manifolds with a four-dimensional isometry group. We then illustrate their geometric properties (with particular regard to curvature, Killing vector fields and their description as Lorentzian Lie groups) and we study several relevant classes of surfaces (parallel, totally umbilical, minimal, constant mean curvature) in these homogeneous Lorentzian three-manifolds.

Keywords

Lorentzian manifoldsBianchi–Cartan–Vranceanu spaceshomogeneous spacestotally umbilical surfacesparallel surfacesminimal and CMC surfaces

MSC classification

Primary: 53B25: Local submanifolds
Secondary: 53C50: Lorentz manifolds, manifolds with indefinite metrics

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , First View , pp. 1 - 23
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc

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Footnotes

Communicated by Graeme Wilkin

References

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