LORENTZIAN SYMMETRIC THREE-SPACES AND THE CLASSIFICATION OF THEIR PARALLEL SURFACES-Reference-Cited by-同舟云学术

LORENTZIAN SYMMETRIC THREE-SPACES AND THE CLASSIFICATION OF THEIR PARALLEL SURFACES

Published:2009-10 Issue:10 Volume:20 Page:1185-1205
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

CALVARUSO G.¹,VAN DER VEKEN J.²

Affiliation:

1. Università del Salento, Dipartimento di Matematica "E. De Giorgi", Provinciale Lecce–Arnesano, 73100 Lecce, Italy

2. Katholieke Universiteit Leuven, Departement Wiskunde, Celestijnenlaan 200 B, B-3001 Leuven, Belgium

Abstract

We describe a global model for Lorentzian symmetric three-spaces admitting a parallel null vector field, and classify completely the surfaces with parallel second fundamental form in all Lorentzian symmetric three-spaces. Interesting differences arise with respect to the Riemannian case studied in [2]. Our results complete the classification of parallel surfaces in all three-dimensional Lorentzian homogeneous spaces.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X09005728

Reference20 articles.

1. On symmetric submanifolds of spaces of constant curvature

2. Surfaces with parallel second fundamental form in Bianchi-Cartan-Vranceanu spaces

3. Symmetric immersions in pseudo-Riemannian space forms

4. On curvature homogeneous three-dimensional Lorentzian manifolds

5. Lorentzian symmetric spaces

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